Solver not applicable (logdetppa)
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Andreas Steimer
Nov 24, 2016, 10:24:26 AM11/24/16
to YALMIP
Hi all,
I am trying to implement the Latent Variable Graphical Model Selection Method of Chandrasekran et al. 2010, the objective of which can be solved by some Newton-CG primal proximal point algorithm.
Based on the following code, I have tested YALMIB for the sake of some toy example (based on some Covariance matrix S0), but to no avail so far:
lam = 0;
gam = 1;
K0 = sdpvar(2,2);
L = sdpvar(2,2);
S0 = sdpvar(2,2);
assign( S0, [1.6943 -0.1030; -0.1030 0.3980] );
constraints = [K0>=0, L>=0];
objective = trace( (K0-L)*S0 ) - logdet(K0-L) + lam*( gam*sum(abs(K0(:))) + trace(L) );
optimize( constraints, objective, sdpsettings('solver','logdetppa','debug',1) )
Execution of this piece of code just results in the error message 'Solver not applicable (logdetppa)'. Changing the solver to 'sdpt3' doesn't change the picture, except for 'logdetppa' being replaced by 'sdpt3'.
Do you have an idea why this is not working? Any help is appreciated...
best,
Andreas
Johan Löfberg
Nov 24, 2016, 11:05:49 AM11/24/16
to YALMIP
your model is nonlinear nonconvex as you have bilinear product trace( (K0-L)*S0 )
Andreas Steimer
Nov 24, 2016, 4:06:19 PM11/24/16
to YALMIP
Much thanks for your prompt reply.
What I don't understand is why expression 'trace( (K0-L)*S0 )' should be nonlinear. 'S0' is not a variable, it has been fixed in advance, thus no quadratic terms emerge in the trace. Also, the problem has been labeled as convex in Chandrasekarans original publication ('LATENT VARIABLE GRAPHICAL MODEL SELECTION VIA CONVEX OPTIMIZATION'), and a Newton-CG primal proximal point algorithm is claimed to be an efficient solver for it in Dauwels et al. 2011 ('Inferring Brain Networks through Graphical Models with Hidden Variables').
Thanks for your patience with someone unfamiliar with optimization algorithms...
best,
Andreas
What I don't understand is why expression 'trace( (K0-L)*S0 )' should be nonlinear. 'S0' is not a variable, it has been fixed in advance, thus no quadratic terms emerge in the trace. Also, the problem has been labeled as convex in Chandrasekarans original publication ('LATENT VARIABLE GRAPHICAL MODEL SELECTION VIA CONVEX OPTIMIZATION'), and a Newton-CG primal proximal point algorithm is claimed to be an efficient solver for it in Dauwels et al. 2011 ('Inferring Brain Networks through Graphical Models with Hidden Variables').
Thanks for your patience with someone unfamiliar with optimization algorithms...
best,
Andreas
Johan Löfberg
Nov 24, 2016, 4:09:39 PM11/24/16
to YALMIP
Huh?
hence, a decision variable
assign is a command to define an initial guess specified for some nonlinear solvers capable of using initial guesses
S0 = sdpvar(2,2);
assign is a command to define an initial guess specified for some nonlinear solvers capable of using initial guesses
Andreas Steimer
Nov 24, 2016, 4:16:20 PM11/24/16
to YALMIP
Ah, I see...
Seems as if we are getting close to the core of the problem.
So how can I define fixed matrices then? I am new to YALMIP, so please excuse my ignorance...
Seems as if we are getting close to the core of the problem.
So how can I define fixed matrices then? I am new to YALMIP, so please excuse my ignorance...
Johan Löfberg
Nov 24, 2016, 4:26:55 PM11/24/16
to YALMIP
S0=[1.6943 -0.1030; -0.1030 0.3980]
yalmip is 99.99% standard matlab syntax
Andreas Steimer
Nov 24, 2016, 4:30:26 PM11/24/16
to YALMIP
Thanks Johan, seems you've made my day. Thumbs up...
Senaka Wijayakoon
Oct 2, 2018, 3:22:25 AM10/2/18
to YALMIP
Hi John
Can you please tell me a non linear solver which can be used in YALMIP+MATLAB to solve non linear LMI as coded bellow. I have faced same problem for following code. I think in this code, term (alpha*P) makes an non linear situation (Highlighted yellow color).
num=0.01;
den=[1 0.2 0.01];
G=tf(num,den);
SYS=ss(G);
A=SYS.A;
B=SYS.B;
C=SYS.C;
%Defining Matrix Variables
P=sdpvar(n);
F=sdpvar(1,1);
alpha=sdpvar(1);
%making a random symmetric positive definite matrix
n=length(A);
Q0 = rand(n,n);
Q0 = 0.5*(Q0+Q0');
Q0 = Q0 + n*eye(n);
%solving Riccati equation to find X
[X,L,GG] = care(A,B,Q0);
%X is not a variable while P, alpha and F are matrix variables
M11=(A'*P)+(P*A)-(X*B*B'*P)-(P*B*B'*X)+(X*B*B'*X)-(alpha*P);
M12=((B'*P)+(F*C))';
M21=(B'*P)+(F*C);
M22=-eye(1,1);
M=[M11 M12;M21 M22];
%defining needed constraints
constr = [(M<=0),(0<=P)];
%select solver
options = sdpsettings('solver','mosek');
%solve LMI by minimizing alpha
optimize(constr,alpha,options);
Thank you
Johan Löfberg
Oct 2, 2018, 3:25:57 AM10/2/18
to YALMIP
First, calling something a nonlinear LMI makes no sense,
Senaka Wijayakoon
Oct 2, 2018, 3:48:35 AM10/2/18
to YALMIP
Hello John
Many thanks for your quick response
I meant alpha and P are both matrix variables, their product (alpha*P) coming within the LMI matrix M is an non linear. That is why I thought it is an non linear component. Then why, solver like mosek is not applicable to minimize the value of alpha while considering LMI [(M<=0),(0<=P)]???. If we set P as a constant (ex:- P=[1 2;3 4]) then solver can minimize alpha properly for LMI (M<=0). When both become variables (P and alpha) this problem 'solver not applicable ' problem arises.
Thank you
Johan Löfberg
Oct 2, 2018, 3:51:39 AM10/2/18
to YALMIP
It is nonlinear, but quasi-convex and can be solved precisely as described in the two articles.
It makes no sense to talk about a nonlinear linear matrix inequality. It's like talking about living dead people.
Senaka Wijayakoon
Oct 2, 2018, 4:41:39 AM10/2/18
to YALMIP
Many thanks John for your kind help
Senaka Wijayakoon
Oct 4, 2018, 1:08:58 AM10/4/18
to YALMIP
Hello Johan
I got a problem with function bisection. fault message is 'Failed to initialize bisection space (bisection)'. This is a non linear case due to alpha*P term. Can you tell me please the reason. Code is as follows
Here Abar is a 12x12 matrix (not variable)
Bbar is a 12x2 matrix (not variable)
Cbar is a 6x12 matrix (not variable)
X is a 12x12 matrix (not variable)
Only P, F and alpha are variables as follows
P=sdpvar(12);
F=sdpvar(2,6);
alpha=sdpvar(1);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
M=[M11 M12;M21 M22];
%defining needed constraints
constr = [(M<=0),(0<=P)];
%select solver
options = sdpsettings('solver','mosek');
%solve LMI by minimizing alpha
diagnostics = bisection(constr,alpha,options)
Thank you
Johan Löfberg
Oct 4, 2018, 1:57:36 AM10/4/18
to YALMIP
For generic random data it works here
Your error message is issued if YALMIP tries to find an upper bound on alpha, but fails to do so (i.e. your specific problem is infeasible, YALMIP tries up to alpha = 1e6 but gives up if that is still infeasible, You can easily confirm this by using alpha 1e6 and see that it is infeasible)
Abar = randn(12,12);Abar = Abar - 20*eye(12);Bbar = randn(12,2);Cbar = randn(6,12);X = randn(12,12);X = X*X';Senaka Wijayakoon
Oct 4, 2018, 2:23:45 AM10/4/18
to YALMIP
Hi Johan
Many thanks for your reply.
But here alpha should be a variable. full code is as follows
num11=-0.37237;
den11=[0.0797 5.689 1 0];
G11=tf(num11,den11);
num12=0.019761;
den12=[301.091 27.693 1 0];
G12=tf(num12,den12);
num21=-0.2018;
den21=[6.315 4.5234 1 0];
G21=tf(num21,den21);
num22=-0.07345;
den22=[16.112 3.523 1 0];
G22=tf(num22,den22);
GMIMO=[G11 G12;G21 G22];
SYS=ss(GMIMO,'minimal');
A=SYS.A;
B=SYS.B;
C=SYS.C;
delta=0;
[~,l]=size(B);%no of inputs
[m,~]=size(C);%no of outputs
%making a random symmetric positive definite matrix
n=length(A);%no of states
Q0 = rand((n+m),(n+m));
Q0 = 0.5*(Q0+Q0');
Q0 = Q0 + (n+m)*eye(n+m);
P=sdpvar(n+m);
F=sdpvar(l,3*m);
alpha=sdpvar(1);
Abar=[A zeros(n,m);C zeros(m,m)];
Bbar=[B;zeros(m,l)];
C1=[C zeros(m,m)];
C2=[zeros(m,n) eye(m,m)];
C3=[(C*A) zeros(m,m)];
Cbar=[C1' C2' C3']';
%solving Riccati equation
[X,L,GG] = care(Abar,Bbar,Q0);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
M=[M11 M12;M21 M22];
%defining needed constraints
constr = [(M<=0),(0<=P)];
%select solver
options = sdpsettings('solver','lmilab');
%solve LMI by minimiying alpha
diagnostics = bisection(constr,alpha,options)
alphasol=double(alpha)
Fsol=double(F)
Can you please check this out
Thank you
Johan Löfberg
Oct 4, 2018, 2:31:51 AM10/4/18
to YALMIP
You cannot use lmilab. It lacks functionality so it cannot be used robustly with YALMIP, in particular in bisection where feasibility info is central.
The problem is easily solved using mosek or sdpt3 (problem appears numerically challenging for sedumi). Note that you are specifying the solver in the wrong way, so you have effectively not specified any solver
%select solveroptions = sdpsettings('bisection.solver','mosek');
%solve LMI by minimiying alphadiagnostics = bisection(constr,alpha,options)Selected solver: MOSEK-SDPIteration Lower bound Test Upper bound Gap Status at test 1 : -1.00000E+00 -5.00000E-01 -0.00000E+00 1.00000E+00 Successfully solved 2 : -1.00000E+00 -7.50000E-01 -5.00000E-01 5.00000E-01 Infeasible problem 3 : -7.50000E-01 -6.25000E-01 -5.00000E-01 2.50000E-01 Successfully solved 4 : -7.50000E-01 -6.87500E-01 -6.25000E-01 1.25000E-01 Successfully solved 5 : -7.50000E-01 -7.18750E-01 -6.87500E-01 6.25000E-02 Successfully solved 6 : -7.50000E-01 -7.34375E-01 -7.18750E-01 3.12500E-02 Infeasible problem 7 : -7.34375E-01 -7.26563E-01 -7.18750E-01 1.56250E-02 Infeasible problem 8 : -7.26563E-01 -7.22656E-01 -7.18750E-01 7.81250E-03 Infeasible problem 9 : -7.22656E-01 -7.20703E-01 -7.18750E-01 3.90625E-03 Successfully solved 10 : -7.22656E-01 -7.21680E-01 -7.20703E-01 1.95313E-03 Successfully solved 11 : -7.22656E-01 -7.22168E-01 -7.21680E-01 9.76563E-04 Successfully solved 12 : -7.22656E-01 -7.22412E-01 -7.22168E-01 4.88281E-04 Successfully solved 13 : -7.22656E-01 -7.22534E-01 -7.22412E-01 2.44141E-04 Successfully solved 14 : -7.22656E-01 -7.22595E-01 -7.22534E-01 1.22070E-04 Successfully solved 15 : -7.22656E-01 -7.22626E-01 -7.22595E-01 6.10352E-05 Successfully solved 16 : -7.22656E-01 -7.22641E-01 -7.22626E-01 3.05176E-05 Successfully solved 17 : -7.22656E-01 -7.22649E-01 -7.22641E-01 1.52588E-05 Unknown error (looks like failure)
diagnostics =
struct with fields:
yalmiptime: 9.9626 solvertime: 0.72323 info: 'Successfully solved (bisection)' problem: 0Senaka Wijayakoon
Oct 4, 2018, 3:48:04 AM10/4/18
to YALMIP
Hello Johan
Thank you for your reply. Unfortunately I am having same message even after following your instructions. Can you please run this code in your machine to confirm what this problem is. Some time there may be a problem with MATLAB or MOSEK. Thank you.
num11=-0.37237;
den11=[0.0797 5.689 1 0];
G11=tf(num11,den11);
num12=0.019761;
den12=[301.091 27.693 1 0];
G12=tf(num12,den12);
num21=-0.2018;
den21=[6.315 4.5234 1 0];
G21=tf(num21,den21);
num22=-0.07345;
den22=[16.112 3.523 1 0];
G22=tf(num22,den22);
GMIMO=[G11 G12;G21 G22];
SYS=ss(GMIMO,'minimal');
A=SYS.A;
B=SYS.B;
C=SYS.C;
delta=0;
%defining matrix variables
[~,l]=size(B);%no of inputs
[m,~]=size(C);%no of outputs
%making a random symmetric positive definite matrix
n=length(A);%no of states
Q0 = rand((n+m),(n+m));
Q0 = 0.5*(Q0+Q0');
Q0 = Q0 + (n+m)*eye(n+m);
P=sdpvar(n+m);
F=sdpvar(l,3*m);
alpha=sdpvar(1);
Abar=[A zeros(n,m);C zeros(m,m)];
Bbar=[B;zeros(m,l)];
C1=[C zeros(m,m)];
C2=[zeros(m,n) eye(m,m)];
C3=[(C*A) zeros(m,m)];
Cbar=[C1' C2' C3']';
>> [X,L,GG] = care(Abar,Bbar,Q0);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
M=[M11 M12;M21 M22];
%defining needed constraints
constr = [(M<=0),(0<=P)];
%select solver
options = sdpsettings('bisection.solver','mosek');
%solve LMI by minimiying alpha
diagnostics = bisection(constr,alpha,options);
>> diagnostics = bisection(constr,alpha,options)
diagnostics =
struct with fields:
yalmiptime: 3.2690
solvertime: 0.4814
info: 'Failed to initialize bisection space (bisection)'
problem: 21
Johan Löfberg
Oct 4, 2018, 3:51:27 AM10/4/18
to YALMIP
Solved easily
so
1. Are you using the latest version of YALMIP
2. Have you checked that mosek actually works
Senaka Wijayakoon
Oct 4, 2018, 4:01:23 AM10/4/18
to YALMIP
1. Yes I got the latest version from https://yalmip.github.io/download/
2. I believe mosek should work properly. Any way ,can you please tell me how to check mosek actually works. I am using a trial version of it.
Johan Löfberg
Oct 4, 2018, 4:02:51 AM10/4/18
to YALMIP
mosekdiag
or simply run a trivial problem optimize(sdpvar(2)>=0,[],sdpsettings('solver','mosek'))
Senaka Wijayakoon
Oct 4, 2018, 4:10:16 AM10/4/18
to YALMIP
Please see highlighted warning
1.
mosekdiag
Matlab version: 9.3.0.713579 (R2017b)
Architecture : PCWIN64
The mosek optimizer executed successfully from the command line:
MOSEK Version 8.1.0.63 (Build date: 2018-9-5 20:39:09)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
FlexLM
Version : 11.14
Hostname : DedicatedMATLAB
Host ID : 3417ebb5473d
License path : C:\Users\Bandara\mosek\mosek.lic
Operating system variables
PATH :
*** No input file specfied. No optimization is performed.
Return code - 0 [MSK_RES_OK]
mosekopt: C:\Program Files\Mosek\8\toolbox\r2014a\mosekopt.mexw64
Found MOSEK version : major(8), minor(1), revision(63)
mosekopt is working correctly.
Warning: MOSEK Fusion is not configured correctly; check that mosek.jar is added to the javaclasspath.
> In mosekdiag (line 85)
2.
optimize(sdpvar(2)>=0,[],sdpsettings('solver','mosek'))
MOSEK Version 8.1.0.63 (Build date: 2018-9-5 20:39:09)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 3
Cones : 0
Scalar variables : 0
Matrix variables : 1
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 3
Cones : 0
Scalar variables : 0
Matrix variables : 1
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 3
Optimizer - Cones : 0
Optimizer - Scalar variables : 0 conic : 0
Optimizer - Semi-definite variables: 1 scalarized : 3
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 6 after factor : 6
Factor - dense dim. : 0 flops : 6.00e+01
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.05
1 0.0e+00 0.0e+00 0.0e+00 1.00e+00 0.000000000e+00 0.000000000e+00 0.0e+00 0.13
Optimizer terminated. Time: 0.17
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 0e+00 barvar: 0e+00
Dual. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 barvar: 0e+00
Optimizer summary
Optimizer - time: 0.17
Interior-point - iterations : 1 time: 0.13
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
ans =
struct with fields:
yalmiptime: 0.5069
solvertime: 0.2801
info: 'Successfully solved (MOSEK)'
problem: 0
Johan Löfberg
Oct 4, 2018, 4:16:26 AM10/4/18
to YALMIP
Simply set alpha = 10 and solve problem using mosek with sdpsettings('solver','mosek','debug',1))
If that doesn't work, it is your mosek installation (although it looks fine).
If it does work, install develop version of YALMIP https://github.com/yalmip/YALMIP/archive/develop.zip which has improved error detection in bisection and see what happens
Senaka Wijayakoon
Oct 4, 2018, 8:25:20 AM10/4/18
to YALMIP
Hello Johan
If we set alpha to a fix value as you have mentioned, then how is it optimized or minimized by the solver? because it is not a variable any more. Are you proposing to do it as an initial value of alpha?. Any way I followed you and got an error message as shown at the end highlighted texts.
% alpha=1e06;
Abar=[A zeros(n,m);C zeros(m,m)];
Bbar=[B;zeros(m,l)];
C1=[C zeros(m,m)];
C2=[zeros(m,n) eye(m,m)];
C3=[(C*A) zeros(m,m)];
Cbar=[C1' C2' C3']';
>> alpha=10;
>> [X,L,GG] = care(Abar,Bbar,Q0);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
M=[M11 M12;M21 M22];
>> constr = [(M<=0),(0<=P)];
>> options=sdpsettings('solver','mosek','debug',1);
>> diagnostics = bisection(constr,alpha,options)
Undefined function or variable 'diagnostic'.
Error in bisection (line 47)
diagnostic.yalmiptime = toc(solvertime)-diagnostic.solvertime;
Johan Löfberg
Oct 4, 2018, 8:30:15 AM10/4/18
to YALMIP
It's not. The idea with that test is to see if mosek behaves as expected when you solve the type of problem which bisection will solve (the command bisection is just a convenient way to perform bisection over different fixed alpha)
You should fix alpha, and then solve the LMI using mosek in the test
diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1))
Senaka Wijayakoon
Oct 4, 2018, 8:54:20 AM10/4/18
to YALMIP
It shows an MOSEK error message which I have highlighted. Is this an expected result to confirm MOSEK works fine?
>> alpha=10;
>> Abar=[A zeros(n,m);C zeros(m,m)];
Bbar=[B;zeros(m,l)];
C1=[C zeros(m,m)];
C2=[zeros(m,n) eye(m,m)];
C3=[(C*A) zeros(m,m)];
Cbar=[C1' C2' C3']';
>> [X,L,GG] = care(Abar,Bbar,Q0);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
M=[M11 M12;M21 M22];
%defining needed constraints
constr = [(M<=0),(0<=P)];
>> diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1))
MOSEK Version 8.1.0.63 (Build date: 2018-9-5 20:39:09)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (13) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (27) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (41) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (55) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (69) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (83) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (97) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (111) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (125) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (139) of matrix 'A'.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.01
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 86
Optimizer - Cones : 0
Optimizer - Scalar variables : 126 conic : 0
Optimizer - Semi-definite variables: 1 scalarized : 78
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 3397 after factor : 3489
Factor - dense dim. : 0 flops : 2.65e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.1e+02 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.03
1 2.5e-01 7.7e+01 1.7e-01 -7.52e-01 -9.901731528e+01 0.000000000e+00 2.5e-01 0.13
2 8.1e-02 2.5e+01 4.3e-02 -3.00e-01 -1.969644101e+02 0.000000000e+00 8.1e-02 0.14
3 2.5e-02 7.9e+00 7.8e-03 -8.78e-01 -6.503255977e+02 0.000000000e+00 2.5e-02 0.14
4 9.1e-03 2.9e+00 2.4e-03 -3.67e-01 -8.825288711e+02 0.000000000e+00 9.1e-03 0.14
5 3.6e-03 1.1e+00 2.5e-04 -1.08e+00 -1.360575615e+04 0.000000000e+00 3.6e-03 0.16
6 1.2e-03 3.8e-01 3.8e-05 -4.08e+00 -6.379551555e+04 0.000000000e+00 1.2e-03 0.16
7 2.8e-04 8.7e-02 2.4e-06 -1.83e+00 -8.863934052e+05 0.000000000e+00 2.8e-04 0.16
8 7.2e-05 2.3e-02 2.0e-07 -1.95e+00 -8.273406207e+06 0.000000000e+00 7.2e-05 0.16
9 1.7e-05 5.4e-03 1.6e-08 -1.46e+00 -7.119027889e+07 0.000000000e+00 1.7e-05 0.17
10 4.6e-06 1.4e-03 1.9e-09 -1.26e+00 -3.799101659e+08 0.000000000e+00 4.6e-06 0.17
11 1.8e-06 5.6e-04 6.1e-10 -8.30e-01 -5.532210869e+08 0.000000000e+00 1.8e-06 0.17
12 6.6e-07 2.1e-04 1.7e-10 -2.46e-01 -9.190285271e+08 0.000000000e+00 6.6e-07 0.19
13 2.1e-07 6.6e-05 2.8e-11 -9.45e-01 -3.584415396e+09 0.000000000e+00 2.1e-07 0.19
14 7.3e-08 2.3e-05 6.1e-12 -8.05e-01 -9.116274483e+09 0.000000000e+00 7.3e-08 0.19
15 1.8e-08 5.6e-06 9.5e-13 -8.35e-01 -2.281883015e+10 0.000000000e+00 1.8e-08 0.20
16 5.2e-09 1.6e-06 4.2e-13 2.09e-01 -1.013021135e+10 0.000000000e+00 5.2e-09 0.20
17 1.1e-09 3.3e-07 1.0e-13 2.50e-01 -7.159577313e+09 0.000000000e+00 1.1e-09 0.20
18 2.1e-10 6.6e-08 2.2e-14 1.51e-01 -6.052861787e+09 0.000000000e+00 2.1e-10 0.20
19 9.2e-11 1.3e-08 4.1e-15 6.02e-02 -6.390099457e+09 0.000000000e+00 4.1e-11 0.22
20 3.6e-11 5.8e-09 1.7e-15 -6.28e-02 -7.952910325e+09 0.000000000e+00 1.8e-11 0.22
21 1.1e-11 1.8e-09 5.6e-16 -1.87e-01 -7.110307001e+09 0.000000000e+00 5.9e-12 0.22
22 4.4e-12 1.7e-09 2.2e-16 4.77e-02 -8.090430353e+09 0.000000000e+00 2.5e-12 0.22
23 3.4e-12 2.4e-08 5.9e-17 -1.02e-01 -7.371693747e+09 0.000000000e+00 6.3e-13 0.23
24 1.5e-12 1.3e-07 2.1e-17 6.21e-02 -8.085751516e+09 0.000000000e+00 2.4e-13 0.23
25 8.0e-13 2.6e-07 6.6e-18 -2.91e-02 -7.176227852e+09 0.000000000e+00 7.0e-14 0.23
26 3.6e-13 1.6e-06 2.7e-18 2.57e-02 -8.322343047e+09 0.000000000e+00 3.1e-14 0.23
27 3.1e-13 2.8e-06 2.2e-18 -1.14e-01 -8.278395653e+09 0.000000000e+00 2.5e-14 0.25
28 1.7e-13 1.1e-06 5.6e-19 -7.28e-02 -7.871800871e+09 0.000000000e+00 6.3e-15 0.25
29 1.6e-13 1.3e-06 4.0e-19 6.42e-02 -7.900009206e+09 0.000000000e+00 4.4e-15 0.25
30 1.2e-13 1.1e-05 3.2e-19 3.06e-02 -7.908911972e+09 0.000000000e+00 3.6e-15 0.27
31 5.6e-14 4.5e-06 7.8e-20 2.11e-02 -8.013703746e+09 0.000000000e+00 8.8e-16 0.27
32 5.5e-14 3.5e-06 7.6e-20 -4.01e-02 -8.012899301e+09 0.000000000e+00 8.6e-16 0.27
33 5.5e-14 3.5e-06 7.6e-20 -3.84e-02 -8.012899301e+09 0.000000000e+00 8.6e-16 0.27
Optimizer terminated. Time: 0.34
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.1429681939e-02 nrm: 8e+01 Viol. con: 2e-11 var: 2e-14 barvar: 0e+00
Optimizer summary
Optimizer - time: 0.34
Interior-point - iterations : 34 time: 0.28
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Mosek error: MSK_RES_TRM_STALL ()
diagnostics =
struct with fields:
yalmiptime: 0.4835
solvertime: 0.5155
info: 'Infeasible problem (MOSEK)'
problem: 1
Johan Löfberg
Oct 4, 2018, 9:02:36 AM10/4/18
to YALMIP
I have no idea why it is infeasible on your machine
run
diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1,'savedebug'))
and send the file mosekdebug.mat to me
Johan Löfberg
Oct 4, 2018, 9:04:01 AM10/4/18
to YALMIP
'savedebug',1
Johan Löfberg
Oct 4, 2018, 9:21:17 AM10/4/18
to YALMIP
Also run once with presolve turned off
diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1,'mosek.MSK_IPAR_PRESOLVE_USE','MSK_OFF'))
to see if it is a presolve bug in your mosek version (the reduced model size is not the same in your model as in mine as displayed by mosek)
Johan Löfberg
Oct 4, 2018, 9:33:22 AM10/4/18
to YALMIP
you can also test with numerical noise eliminated, to see if that is causing some weird issue in your mosek version
constr = [(clean(M,1e-6)<=0),(0<=P)];
Senaka Wijayakoon
Oct 4, 2018, 9:33:39 AM10/4/18
to YALMIP
diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1,'savedebug',1))
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 86
Optimizer - Cones : 0
Optimizer - Scalar variables : 126 conic : 0
Optimizer - Semi-definite variables: 1 scalarized : 78
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 3397 after factor : 3489
Factor - dense dim. : 0 flops : 2.65e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.1e+02 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.03
1 2.5e-01 7.7e+01 1.7e-01 -7.52e-01 -9.901731528e+01 0.000000000e+00 2.5e-01 0.11
2 8.1e-02 2.5e+01 4.3e-02 -3.00e-01 -1.969644101e+02 0.000000000e+00 8.1e-02 0.11
3 2.5e-02 7.9e+00 7.8e-03 -8.78e-01 -6.503255977e+02 0.000000000e+00 2.5e-02 0.11
4 9.1e-03 2.9e+00 2.4e-03 -3.67e-01 -8.825288711e+02 0.000000000e+00 9.1e-03 0.13
5 3.6e-03 1.1e+00 2.5e-04 -1.08e+00 -1.360575615e+04 0.000000000e+00 3.6e-03 0.13
6 1.2e-03 3.8e-01 3.8e-05 -4.08e+00 -6.379551555e+04 0.000000000e+00 1.2e-03 0.13
7 2.8e-04 8.7e-02 2.4e-06 -1.83e+00 -8.863934052e+05 0.000000000e+00 2.8e-04 0.13
8 7.2e-05 2.3e-02 2.0e-07 -1.95e+00 -8.273406207e+06 0.000000000e+00 7.2e-05 0.14
9 1.7e-05 5.4e-03 1.6e-08 -1.46e+00 -7.119027889e+07 0.000000000e+00 1.7e-05 0.14
10 4.6e-06 1.4e-03 1.9e-09 -1.26e+00 -3.799101659e+08 0.000000000e+00 4.6e-06 0.14
11 1.8e-06 5.6e-04 6.1e-10 -8.30e-01 -5.532210869e+08 0.000000000e+00 1.8e-06 0.14
12 6.6e-07 2.1e-04 1.7e-10 -2.46e-01 -9.190285271e+08 0.000000000e+00 6.6e-07 0.14
13 2.1e-07 6.6e-05 2.8e-11 -9.45e-01 -3.584415396e+09 0.000000000e+00 2.1e-07 0.16
14 7.3e-08 2.3e-05 6.1e-12 -8.05e-01 -9.116274483e+09 0.000000000e+00 7.3e-08 0.16
15 1.8e-08 5.6e-06 9.5e-13 -8.35e-01 -2.281883015e+10 0.000000000e+00 1.8e-08 0.16
16 5.2e-09 1.6e-06 4.2e-13 2.09e-01 -1.013021135e+10 0.000000000e+00 5.2e-09 0.16
17 1.1e-09 3.3e-07 1.0e-13 2.50e-01 -7.159577313e+09 0.000000000e+00 1.1e-09 0.17
18 2.1e-10 6.6e-08 2.2e-14 1.51e-01 -6.052861787e+09 0.000000000e+00 2.1e-10 0.17
19 9.2e-11 1.3e-08 4.1e-15 6.02e-02 -6.390099457e+09 0.000000000e+00 4.1e-11 0.17
20 3.6e-11 5.8e-09 1.7e-15 -6.28e-02 -7.952910325e+09 0.000000000e+00 1.8e-11 0.17
21 1.1e-11 1.8e-09 5.6e-16 -1.87e-01 -7.110307001e+09 0.000000000e+00 5.9e-12 0.19
22 4.4e-12 1.7e-09 2.2e-16 4.77e-02 -8.090430353e+09 0.000000000e+00 2.5e-12 0.19
23 3.4e-12 2.4e-08 5.9e-17 -1.02e-01 -7.371693747e+09 0.000000000e+00 6.3e-13 0.19
24 1.5e-12 1.3e-07 2.1e-17 6.21e-02 -8.085751516e+09 0.000000000e+00 2.4e-13 0.19
25 8.0e-13 2.6e-07 6.6e-18 -2.91e-02 -7.176227852e+09 0.000000000e+00 7.0e-14 0.20
26 3.6e-13 1.6e-06 2.7e-18 2.57e-02 -8.322343047e+09 0.000000000e+00 3.1e-14 0.20
27 3.1e-13 2.8e-06 2.2e-18 -1.14e-01 -8.278395653e+09 0.000000000e+00 2.5e-14 0.20
28 1.7e-13 1.1e-06 5.6e-19 -7.28e-02 -7.871800871e+09 0.000000000e+00 6.3e-15 0.20
29 1.6e-13 1.3e-06 4.0e-19 6.42e-02 -7.900009206e+09 0.000000000e+00 4.4e-15 0.22
30 1.2e-13 1.1e-05 3.2e-19 3.06e-02 -7.908911972e+09 0.000000000e+00 3.6e-15 0.22
31 5.6e-14 4.5e-06 7.8e-20 2.11e-02 -8.013703746e+09 0.000000000e+00 8.8e-16 0.22
32 5.5e-14 3.5e-06 7.6e-20 -4.01e-02 -8.012899301e+09 0.000000000e+00 8.6e-16 0.22
33 5.5e-14 3.5e-06 7.6e-20 -3.84e-02 -8.012899301e+09 0.000000000e+00 8.6e-16 0.23
Optimizer terminated. Time: 0.28
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.1429681939e-02 nrm: 8e+01 Viol. con: 2e-11 var: 2e-14 barvar: 0e+00
Optimizer summary
Optimizer - time: 0.28
Interior-point - iterations : 34 time: 0.23
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Mosek error: MSK_RES_TRM_STALL ()
diagnostics =
struct with fields:
yalmiptime: 0.1717
solvertime: 0.4383
Senaka Wijayakoon
Oct 4, 2018, 9:34:15 AM10/4/18
to YALMIP
diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1,'mosek.MSK_IPAR_PRESOLVE_USE','MSK_OFF'))
MOSEK Version 8.1.0.63 (Build date: 2018-9-5 20:39:09)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (13) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (27) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (41) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (55) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (69) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (83) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (97) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (111) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (125) of matrix 'A'.
MOSEK warning 710: #8 (nearly) zero elements are specified in sparse col '' (139) of matrix 'A'.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer started.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 90
Optimizer - Cones : 0
Optimizer - Scalar variables : 192 conic : 0
Optimizer - Semi-definite variables: 1 scalarized : 78
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 3425 after factor : 3517
Factor - dense dim. : 0 flops : 2.87e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.1e+02 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.00
1 2.5e-01 7.7e+01 1.6e-01 -7.63e-01 -1.061587819e+02 0.000000000e+00 2.5e-01 0.08
2 7.0e-02 2.2e+01 2.7e-02 -5.35e-01 -3.880956347e+02 0.000000000e+00 7.0e-02 0.08
3 2.6e-02 8.2e+00 9.9e-03 -7.91e-01 -4.243182677e+02 0.000000000e+00 2.6e-02 0.09
4 1.0e-02 3.1e+00 2.6e-03 -7.94e-01 -9.621393714e+02 0.000000000e+00 1.0e-02 0.09
5 7.4e-03 2.3e+00 7.8e-04 -2.21e+00 -5.715806511e+03 0.000000000e+00 7.4e-03 0.09
6 2.4e-03 7.6e-01 6.8e-05 -2.46e+00 -8.050309727e+04 0.000000000e+00 2.4e-03 0.09
7 6.5e-04 2.0e-01 6.1e-06 -2.30e+00 -7.224217332e+05 0.000000000e+00 6.5e-04 0.11
8 1.6e-04 5.1e-02 4.3e-07 -2.05e+00 -9.328227409e+06 0.000000000e+00 1.6e-04 0.11
9 5.1e-05 1.6e-02 5.9e-08 -1.64e+00 -4.829035717e+07 0.000000000e+00 5.1e-05 0.11
10 1.5e-05 4.8e-03 7.8e-09 -1.43e+00 -2.514049506e+08 0.000000000e+00 1.5e-05 0.11
11 4.9e-06 1.5e-03 1.3e-09 -1.15e+00 -8.807231927e+08 0.000000000e+00 4.9e-06 0.11
12 3.3e-06 1.0e-03 9.4e-10 -6.09e-01 -8.039379072e+08 0.000000000e+00 3.3e-06 0.13
13 9.8e-07 3.1e-04 2.4e-10 -3.38e-01 -1.102187333e+09 0.000000000e+00 9.8e-07 0.13
14 2.6e-07 8.1e-05 2.5e-11 -8.70e-01 -6.694300969e+09 0.000000000e+00 2.6e-07 0.13
15 7.8e-08 2.4e-05 4.0e-12 -9.10e-01 -2.463405605e+10 0.000000000e+00 7.8e-08 0.13
16 2.1e-08 6.7e-06 8.9e-13 -7.77e-01 -3.690234286e+10 0.000000000e+00 2.1e-08 0.14
17 6.2e-09 1.9e-06 3.9e-13 2.80e-01 -1.590550774e+10 0.000000000e+00 6.2e-09 0.14
18 1.3e-09 4.0e-07 9.2e-14 2.31e-01 -1.254932796e+10 0.000000000e+00 1.3e-09 0.14
19 3.0e-10 9.2e-08 2.3e-14 1.33e-01 -1.032004736e+10 0.000000000e+00 3.0e-10 0.14
20 8.2e-11 2.0e-08 4.9e-15 4.76e-02 -1.124146814e+10 0.000000000e+00 6.5e-11 0.16
21 4.8e-11 5.2e-09 1.1e-15 -8.92e-02 -1.523020755e+10 0.000000000e+00 1.7e-11 0.16
22 2.1e-11 2.3e-09 4.3e-16 -6.67e-02 -1.837133685e+10 0.000000000e+00 7.3e-12 0.16
23 1.5e-11 1.7e-08 1.5e-16 -9.03e-02 -1.546624873e+10 0.000000000e+00 2.3e-12 0.16
24 8.1e-12 9.2e-08 5.6e-17 5.83e-02 -1.797804112e+10 0.000000000e+00 9.4e-13 0.17
25 2.7e-12 3.4e-07 1.8e-17 2.60e-04 -1.556042319e+10 0.000000000e+00 2.8e-13 0.17
26 9.0e-13 3.9e-07 6.8e-18 3.83e-02 -1.810763150e+10 0.000000000e+00 1.2e-13 0.17
27 2.1e-13 8.9e-07 2.2e-18 1.82e-02 -1.573383068e+10 0.000000000e+00 3.4e-14 0.17
Optimizer terminated. Time: 0.23
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.8066541375e-01 nrm: 6e+01 Viol. con: 1e-10 var: 9e-13 barvar: 0e+00
Optimizer summary
Optimizer - time: 0.23
Interior-point - iterations : 27 time: 0.19
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
diagnostics =
struct with fields:
yalmiptime: 0.1229
solvertime: 0.3801
Senaka Wijayakoon
Oct 4, 2018, 9:37:48 AM10/4/18
to YALMIP
constr = [(clean(M,1e-6)<=0),(0<=P)];
>> diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1,'savedebug',1))
MOSEK Version 8.1.0.63 (Build date: 2018-9-5 20:39:09)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.02
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 86
Optimizer - Cones : 0
Optimizer - Scalar variables : 126 conic : 0
Optimizer - Semi-definite variables: 1 scalarized : 78
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 3397 after factor : 3489
Factor - dense dim. : 0 flops : 2.65e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.1e+02 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.03
1 2.5e-01 7.7e+01 1.7e-01 -7.52e-01 -9.901731528e+01 0.000000000e+00 2.5e-01 0.11
2 8.1e-02 2.5e+01 4.3e-02 -3.00e-01 -1.969644101e+02 0.000000000e+00 8.1e-02 0.11
3 2.5e-02 7.9e+00 7.8e-03 -8.78e-01 -6.503255977e+02 0.000000000e+00 2.5e-02 0.11
4 9.1e-03 2.9e+00 2.4e-03 -3.67e-01 -8.825288711e+02 0.000000000e+00 9.1e-03 0.13
5 3.6e-03 1.1e+00 2.5e-04 -1.08e+00 -1.360575615e+04 0.000000000e+00 3.6e-03 0.13
6 1.2e-03 3.8e-01 3.8e-05 -4.08e+00 -6.379551555e+04 0.000000000e+00 1.2e-03 0.13
7 2.8e-04 8.7e-02 2.4e-06 -1.83e+00 -8.863934052e+05 0.000000000e+00 2.8e-04 0.13
8 7.2e-05 2.3e-02 2.0e-07 -1.95e+00 -8.273406207e+06 0.000000000e+00 7.2e-05 0.13
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.1429681939e-02 nrm: 8e+01 Viol. con: 2e-11 var: 2e-14 barvar: 0e+00
Optimizer summary
Optimizer - time: 0.28
Interior-point - iterations : 34 time: 0.23
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Mosek error: MSK_RES_TRM_STALL ()
diagnostics =
struct with fields:
yalmiptime: 0.1439
solvertime: 0.3991
Johan Löfberg
Oct 4, 2018, 9:38:46 AM10/4/18
to YALMIP
you were supposed to send the file mosekdebug.mat to me
Senaka Wijayakoon
Oct 4, 2018, 9:39:24 AM10/4/18
to YALMIP
constr = [(clean(M,1e-6)<=0),(0<=P)];
>> diagnostics = optimize(constr,[],sdpsettings('solver','mosek','debug',1,'mosek.MSK_IPAR_PRESOLVE_USE','MSK_OFF'))
MOSEK Version 8.1.0.63 (Build date: 2018-9-5 20:39:09)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer started.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 90
Cones : 0
Scalar variables : 192
Matrix variables : 1
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 90
Optimizer - Cones : 0
Optimizer - Scalar variables : 192 conic : 0
Optimizer - Semi-definite variables: 1 scalarized : 78
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 3425 after factor : 3517
Factor - dense dim. : 0 flops : 2.87e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.1e+02 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.00
1 2.5e-01 7.7e+01 1.6e-01 -7.63e-01 -1.061587819e+02 0.000000000e+00 2.5e-01 0.09
2 7.0e-02 2.2e+01 2.7e-02 -5.35e-01 -3.880956347e+02 0.000000000e+00 7.0e-02 0.09
3 2.6e-02 8.2e+00 9.9e-03 -7.91e-01 -4.243182677e+02 0.000000000e+00 2.6e-02 0.09
4 1.0e-02 3.1e+00 2.6e-03 -7.94e-01 -9.621393714e+02 0.000000000e+00 1.0e-02 0.09
5 7.4e-03 2.3e+00 7.8e-04 -2.21e+00 -5.715806511e+03 0.000000000e+00 7.4e-03 0.11
6 2.4e-03 7.6e-01 6.8e-05 -2.46e+00 -8.050309727e+04 0.000000000e+00 2.4e-03 0.11
7 6.5e-04 2.0e-01 6.1e-06 -2.30e+00 -7.224217332e+05 0.000000000e+00 6.5e-04 0.11
8 1.6e-04 5.1e-02 4.3e-07 -2.05e+00 -9.328227409e+06 0.000000000e+00 1.6e-04 0.11
9 5.1e-05 1.6e-02 5.9e-08 -1.64e+00 -4.829035717e+07 0.000000000e+00 5.1e-05 0.11
10 1.5e-05 4.8e-03 7.8e-09 -1.43e+00 -2.514049506e+08 0.000000000e+00 1.5e-05 0.13
11 4.9e-06 1.5e-03 1.3e-09 -1.15e+00 -8.807231927e+08 0.000000000e+00 4.9e-06 0.13
12 3.3e-06 1.0e-03 9.4e-10 -6.09e-01 -8.039379072e+08 0.000000000e+00 3.3e-06 0.13
13 9.8e-07 3.1e-04 2.4e-10 -3.38e-01 -1.102187333e+09 0.000000000e+00 9.8e-07 0.14
14 2.6e-07 8.1e-05 2.5e-11 -8.70e-01 -6.694300969e+09 0.000000000e+00 2.6e-07 0.14
15 7.8e-08 2.4e-05 4.0e-12 -9.10e-01 -2.463405605e+10 0.000000000e+00 7.8e-08 0.14
16 2.1e-08 6.7e-06 8.9e-13 -7.77e-01 -3.690234286e+10 0.000000000e+00 2.1e-08 0.14
17 6.2e-09 1.9e-06 3.9e-13 2.80e-01 -1.590550774e+10 0.000000000e+00 6.2e-09 0.14
18 1.3e-09 4.0e-07 9.2e-14 2.31e-01 -1.254932796e+10 0.000000000e+00 1.3e-09 0.16
19 3.0e-10 9.2e-08 2.3e-14 1.33e-01 -1.032004736e+10 0.000000000e+00 3.0e-10 0.16
20 8.2e-11 2.0e-08 4.9e-15 4.76e-02 -1.124146814e+10 0.000000000e+00 6.5e-11 0.16
21 4.8e-11 5.2e-09 1.1e-15 -8.92e-02 -1.523020755e+10 0.000000000e+00 1.7e-11 0.16
22 2.1e-11 2.3e-09 4.3e-16 -6.67e-02 -1.837133685e+10 0.000000000e+00 7.3e-12 0.17
23 1.5e-11 1.7e-08 1.5e-16 -9.03e-02 -1.546624873e+10 0.000000000e+00 2.3e-12 0.17
24 8.1e-12 9.2e-08 5.6e-17 5.83e-02 -1.797804112e+10 0.000000000e+00 9.4e-13 0.17
25 2.7e-12 3.4e-07 1.8e-17 2.60e-04 -1.556042319e+10 0.000000000e+00 2.8e-13 0.17
26 9.0e-13 3.9e-07 6.8e-18 3.83e-02 -1.810763150e+10 0.000000000e+00 1.2e-13 0.19
27 2.1e-13 8.9e-07 2.2e-18 1.82e-02 -1.573383068e+10 0.000000000e+00 3.4e-14 0.19
Optimizer terminated. Time: 0.23
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.8066541375e-01 nrm: 6e+01 Viol. con: 1e-10 var: 9e-13 barvar: 0e+00
Optimizer summary
Optimizer - time: 0.23
Interior-point - iterations : 27 time: 0.19
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
diagnostics =
struct with fields:
yalmiptime: 0.0719
solvertime: 0.3531
Johan Löfberg
Oct 4, 2018, 9:54:41 AM10/4/18
to YALMIP
your problem is numerically sensitive leading to non-symmetry on things you would think are symmetric
>> M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P)Linear matrix variable 12x12 (full, real, 78 variables)
>> norm(getbase(M11-M11'),inf)
ans =
1.9323e-11
Johan Löfberg
Oct 4, 2018, 10:01:40 AM10/4/18
to YALMIP
I get completely different data in my model though, so assuming you're really using the most recent release, there must be differences in matlabs code to generate your data
Report
>> Abar
Abar =
Columns 1 through 8
-38.2537 -3.7183 -0.1042 -14.6877 13.4813 6.6874 -24.6399 -4.9530 -4.3918 -0.3332 -0.3937 -1.5858 1.4555 0.7220 -2.6602 -0.5347 -0.4291 0.6005 -0.7943 0.1055 -0.0472 -0.0234 0.0863 0.0173 -16.8199 -1.5684 0.0411 -6.5971 5.8820 2.9650 -10.9248 -2.1960 15.4232 1.4366 -0.0694 6.3089 -5.4809 -2.5005 9.9205 1.9942 7.7247 0.5247 -0.1151 2.8002 -2.7634 -1.4584 4.9525 1.0197 -28.1736 -2.7883 -0.0406 -10.7512 10.0478 5.0831 -18.4221 -3.6961 -5.4796 -1.2128 -0.5901 -2.2995 2.0030 1.1185 -3.7454 -0.7739 -2.4608 -0.3130 -0.0737 -0.9959 0.6346 0.3429 -1.7892 -0.2642 2.3839 0.3334 0.0628 0.7330 -1.6946 -0.1455 1.2806 0.3114 0.9628 1.2260 -0.4648 -0.3605 0.4991 0.1266 -0.8700 -0.3957 -0.0053 -0.0086 0.0021 0.0158 -0.0168 -0.0366 0.0011 -0.1196
Columns 9 through 12
-2.1707 2.0911 0 0 -0.2344 0.2258 0 0 0.0076 -0.0073 0 0 -0.9625 0.9272 0 0 0.8740 -0.8419 0 0 0.4469 -0.4305 0 0 -1.6167 1.5574 0 0 -0.3348 0.3225 0 0 -0.1494 0.1439 0 0 0.1496 -0.1441 0 0 -0.0692 0.0743 0 0 -0.0311 -0.0660 0 0
>> Bbar
Bbar =
1.5342 0.0000 0.0410 0.0080 0.1932 -0.0062 0.5642 -0.1193 -0.5313 -0.0051 -0.2681 -0.0468 0.9720 0.0546 0.1958 -0.0009 0.0858 -0.0000 -0.0827 0.0000 0 0 0 0
>> Q0
Q0 =
Columns 1 through 8
12.6690 0.6662 0.5334 0.3713 0.1807 0.4057 0.3368 0.4977 0.6662 12.6174 0.7185 0.9012 0.3383 0.5841 0.2510 0.3691 0.5334 0.7185 12.9870 0.5478 0.5692 0.0938 0.2556 0.5341 0.3713 0.9012 0.5478 12.4406 0.6743 0.5427 0.3363 0.6079 0.1807 0.3383 0.5692 0.6743 12.1126 0.3506 0.1507 0.4626 0.4057 0.5841 0.0938 0.5427 0.3506 12.2976 0.3070 0.1920 0.3368 0.2510 0.2556 0.3363 0.1507 0.3070 12.1425 0.1682 0.4977 0.3691 0.5341 0.6079 0.4626 0.1920 0.1682 12.4363 0.5090 0.4528 0.3851 0.6063 0.7697 0.5701 0.3636 0.1960 0.5044 0.4809 0.2005 0.5813 0.6569 0.8078 0.3651 0.1793 0.2760 0.3605 0.4204 0.5083 0.2889 0.2828 0.5014 0.7516 0.3392 0.4604 0.7367 0.6514 0.5896 0.7567 0.5384 0.3955
Columns 9 through 12
0.5090 0.5044 0.2760 0.3392 0.4528 0.4809 0.3605 0.4604 0.3851 0.2005 0.4204 0.7367 0.6063 0.5813 0.5083 0.6514 0.7697 0.6569 0.2889 0.5896 0.5701 0.8078 0.2828 0.7567 0.3636 0.3651 0.5014 0.5384 0.1960 0.1793 0.7516 0.3955 12.7724 0.5405 0.2098 0.5399 0.5405 12.4424 0.7285 0.0172 0.2098 0.7285 12.2748 0.2790 0.5399 0.0172 0.2790 12.6996
>> X
X =
1.0e+03 *
Columns 1 through 8
1.8331 2.0056 -1.1186 -0.8082 0.7925 0.3984 -1.6291 -0.4804 2.0056 2.3295 -1.2232 -0.8820 0.8757 0.4439 -1.7828 -0.5883 -1.1186 -1.2232 0.6927 0.4907 -0.4804 -0.2180 1.0077 0.2814 -0.8082 -0.8820 0.4907 0.4453 -0.2567 -0.2601 0.6861 0.2191 0.7925 0.8757 -0.4804 -0.2567 0.5348 0.2534 -0.6241 -0.2549 0.3984 0.4439 -0.2180 -0.2601 0.2534 0.7464 -0.0202 -0.2709 -1.6291 -1.7828 1.0077 0.6861 -0.6241 -0.0202 1.6341 0.3353 -0.4804 -0.5883 0.2814 0.2191 -0.2549 -0.2709 0.3353 0.2218 -0.0645 -0.0881 0.0276 0.0485 -0.0899 -0.2797 -0.0916 0.0906 0.2203 0.2433 -0.1324 -0.1382 0.0323 0.1010 -0.1852 -0.0581 0.4043 0.4601 -0.2453 -0.1754 0.1782 0.0850 -0.3609 -0.1131 -0.3680 -0.3679 0.2287 0.1849 -0.1291 -0.1108 0.3201 0.0672
Columns 9 through 12
-0.0645 0.2203 0.4043 -0.3680 -0.0881 0.2433 0.4601 -0.3679 0.0276 -0.1324 -0.2453 0.2287 0.0485 -0.1382 -0.1754 0.1849 -0.0899 0.0323 0.1782 -0.1291 -0.2797 0.1010 0.0850 -0.1108 -0.0916 -0.1852 -0.3609 0.3201 0.0906 -0.0581 -0.1131 0.0672 0.1956 -0.0298 -0.0164 0.0134 -0.0298 0.0794 0.0482 -0.0687 -0.0164 0.0482 0.1175 -0.0689 0.0134 -0.0687 -0.0689 0.2040
>> L
L =
-71.5638 + 0.0000i -1.0140 + 0.0000i -0.6673 + 0.6439i -0.6673 - 0.6439i -0.6026 + 0.0000i -0.3649 + 0.4846i -0.3649 - 0.4846i -0.1978 + 0.0911i -0.1978 - 0.0911i -0.0670 + 0.0000i -0.0464 + 0.0386i -0.0464 - 0.0386i
>> GG
GG =
Columns 1 through 8
-6.5999 -21.4709 5.8616 1.4045 -4.9059 0.8134 7.7027 6.7827 8.0414 9.2224 -5.1139 -12.4175 -7.9019 -1.2024 -9.1835 -0.4611
Columns 9 through 12
0.7364 -0.3122 -3.1147 -1.7022 1.8124 4.2860 1.6043 -3.1309
Senaka Wijayakoon
Oct 4, 2018, 10:18:54 AM10/4/18
to YALMIP
Hello Johan
Many thanks for your great helps so far. It seems your final symmetric proposal (M11=(M11+M11')/2) is working nicely. Any way could please tell me what your MOSEK version is and where can I download it?. What is your MATLAB version too? is it 64x bits?. Final result after setting alpha as a variable and (M11=(M11+M11')/2) is as follows
alpha=sdpvar(1);
% alpha=1e06;
Abar=[A zeros(n,m);C zeros(m,m)];
Bbar=[B;zeros(m,l)];
C1=[C zeros(m,m)];
C2=[zeros(m,n) eye(m,m)];
C3=[(C*A) zeros(m,m)];
Cbar=[C1' C2' C3']';
>> [X,L,GG] = care(Abar,Bbar,Q0);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
>> M11 = (M11 + M11')/2;
>> M=[M11 M12;M21 M22];
%defining needed constraints
constr = [(M<=0),(0<=P)];
>> diagnostics = bisection(constr,alpha,sdpsettings('solver','mosek','debug',1,'savedebug',1))
Selected solver: MOSEK-SDP
Iteration Lower bound Test Upper bound Gap Status at test
1 : -0.00000E+00 6.25000E-02 1.25000E-01 1.25000E-01 Successfully solved
2 : -0.00000E+00 3.12500E-02 6.25000E-02 6.25000E-02 Successfully solved
3 : -0.00000E+00 1.56250E-02 3.12500E-02 3.12500E-02 Successfully solved
4 : -0.00000E+00 7.81250E-03 1.56250E-02 1.56250E-02 Infeasible problem
5 : 7.81250E-03 1.17188E-02 1.56250E-02 7.81250E-03 Successfully solved
6 : 7.81250E-03 9.76563E-03 1.17188E-02 3.90625E-03 Numerical problems (looks like failure)
7 : 9.76563E-03 1.07422E-02 1.17188E-02 1.95313E-03 Successfully solved
8 : 9.76563E-03 1.02539E-02 1.07422E-02 9.76563E-04 Successfully solved
9 : 9.76563E-03 1.00098E-02 1.02539E-02 4.88281E-04 Unknown error (looks like failure)
10 : 1.00098E-02 1.01318E-02 1.02539E-02 2.44141E-04 Successfully solved
11 : 1.00098E-02 1.00708E-02 1.01318E-02 1.22070E-04 Unknown error (looks like failure)
12 : 1.00708E-02 1.01013E-02 1.01318E-02 6.10352E-05 Unknown error (looks like failure)
13 : 1.01013E-02 1.01166E-02 1.01318E-02 3.05176E-05 Successfully solved
14 : 1.01013E-02 1.01089E-02 1.01166E-02 1.52588E-05 Unknown error (looks like failure)
diagnostics =
struct with fields:
yalmiptime: 4.0084
solvertime: 0.8504
info: 'Successfully solved (bisection)'
problem: 0
>> alphasol=double(alpha)
alphasol =
0.0101
>> Fsol=double(F)
Fsol =
674.3580 -31.6682 457.2575 239.8155 568.5078 795.1818
-2.5101 -17.9303 22.5568 12.3303 -45.3880 134.9198
Johan Löfberg
Oct 4, 2018, 11:24:39 AM10/4/18
to YALMIP
As I said, I think the problem (besides the symmetry loss now corrected) is the fact that you get different data on your machine, thus leading to other optimization problems than what I have. Hence, look at the data and compare to what I wrote (and perhaps save them and post them)
Johan Löfberg
Oct 4, 2018, 2:07:12 PM10/4/18
to YALMIP
I saw now that you have randomized data, so of course we get different results....
With the symmetry fix, it appears to have fixed everything. Works as expected now.
Senaka Wijayakoon
Oct 4, 2018, 10:49:38 PM10/4/18
to YALMIP
Hello Johan
1. In this program our ultimate goal is to find F (variable) and P (variable) while minimizing alpha and considering constr = [(M<=0),(0<=P)]. Could you please tell me whether we should have same results for F and P for different simulation sessions?. I believe they may be different because of it is a quasi-convex problem which is tried to solve from different initial conditions for each session.
2. It seems your machine and my one are still producing different Abar, Bbar and Cbar which depends on only A,B and C matrices. I think according to principles this scenario may also be possible. My transfer function matrix can be converted to different equivalent state space realizations. What is your idea?
Thank you
Johan Löfberg
Oct 5, 2018, 2:12:08 AM10/5/18
to yal...@googlegroups.com
Well if your realization of the model is dependent on matlab version, there is no meaning to compare results on my machine and yours. If I lock Q0 = I, and run your code I get alpha = .0287. If I now do SYS = balreal(SYS) and thus simply create another realization, the problem is extremely easy to satisfy as optimal alpha even is negative, -0.092. Making a simple variable transformation instead by multiplying B with 10 and C with 0.1 i,e still same input-output relation, just a different realization) leads to alpha = 0.19. Your method is not invariant to variable changes, which can happen over different matlab versions
Senaka Wijayakoon
Oct 5, 2018, 6:00:52 AM10/5/18
to YALMIP
Finally I could run whole algorithm for finding a Static Output Feedback (SOF) PID controller. I found 2by2 gain matrices for P,I and D components. F1 for P, F2 for I and F3 for D. Unfortunately control can't follow the step reference input at all. Eventually system's output reaches zero instead of step reference input 1. If you can please run m-file attached with mail ans see it. Results are don't make any sense as an controller. Thank you.
Johan Löfberg
Oct 5, 2018, 7:28:42 AM10/5/18
to YALMIP
it is impossible for anyone but you to know what you are doing. All I can say is when I run your code, I would not trust the result coming out from
constr = [(M<=0),(0<=P),(0<=(eye(size(C*B*f3bar))+(C*B*f3bar)'+(C*B*f3bar)))]; options=sdpsettings('solver','mosek'); optimize(constr,trace(P),options)looking at the diagnostic from mosek and from yalmip, it tells you the results are dubious, and indeed the solution is far from feasible
s =
struct with fields:
yalmipversion: '20180926'
yalmiptime: 0.2651
solvertime: 0.5039
info: 'Numerical problems (MOSEK)'
problem: 4
K>> check(constr)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| ID| Constraint| Primal residual| Dual residual|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| #1| Matrix inequality| -0.0022697| 0.041435|
| #2| Matrix inequality| 4.5606| 0.0030977|
| #3| Matrix inequality| 1| 918.0677|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| A primal-dual optimal solution would show non-negative residuals.|
| In practice, many solvers converge to slightly infeasible |
| solutions, which may cause some residuals to be negative. |
| It is up to the user to judge the importance and impact of |
| slightly negative residuals (i.e. infeasibilities) |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Senaka Wijayakoon
Oct 6, 2018, 9:12:46 AM10/6/18
to YALMIP
Hello Johan
Can you please run the bellow code to see the results for F1,F2,F3 and alpha. If alpha get reduced bellow zero for Q0 identity matrix then results for F should be correct. Here my results make crazy things for SOF-PID. F1,F2 and F3 are proportional, Integral and derivative gain matrices respectively. Output is not following reference step input at all.
num11=-0.37237;
den11=[0.0797 5.689 1 0];
G11=tf(num11,den11);
num12=0.019761;
den12=[301.091 27.693 1 0];
G12=tf(num12,den12);
num21=-0.2018;
den21=[6.315 4.5234 1 0];
G21=tf(num21,den21);
num22=-0.07345;
den22=[16.112 3.523 1 0];
G22=tf(num22,den22);
GMIMO=[G11 G12;G21 G22];
SYS=ss(GMIMO,'minimal');
A=SYS.A;
B=SYS.B;
C=SYS.C;
%defining matrix variables
[~,l]=size(B);%no of inputs
[m,~]=size(C);%no of outputs
%making a random symmetric positive definite matrix
Q0=eye(n+m);
P=sdpvar(n+m);
F=sdpvar(l,3*m);
alpha=sdpvar(1);
Abar=[A zeros(n,m);C zeros(m,m)];
Bbar=[B;zeros(m,l)];
C1=[C zeros(m,m)];
C2=[zeros(m,n) eye(m,m)];
C3=[(C*A) zeros(m,m)];
Cbar=[C1' C2' C3']';
%solving Riccati equation
[X,L,GG] = care(Abar,Bbar,Q0);
%defining matrix to be test for LMI
M11=(Abar'*P)+(P*Abar)-(X*Bbar*Bbar'*P)-(P*Bbar*Bbar'*X)+(X*Bbar*Bbar'*X)-(alpha*P);
M12=((Bbar'*P)+(F*Cbar))';
M21=(Bbar'*P)+(F*Cbar);
[~,nc]=size(M12);
[nr,~]=size(M21);
M22=-eye(nr,nc);
M11=(M11+M11')/2;
M=[M11 M12;M21 M22];
%defining needed constraints
f3bar=F(:,5:6);
constr = [(M<=0),(0<=P),(0<=(eye(size(C*B*f3bar))+(C*B*f3bar)'+(C*B*f3bar)))];
%select solver
options=sdpsettings('solver','mosek','debug',1);
%solve LMI by minimizing alpha
diagnostics = bisection(constr,alpha,options);
alphasol=double(alpha);
Fsol=double(F);
fprintf('The value of F is %d',Fsol);
fprintf('The value of alpha is %d',alphasol);
F1bar=Fsol(:,1:2);
F2bar=Fsol(:,3:4);
F3bar=Fsol(:,5:6);
F3=F3bar*inv(eye(size(C*B*F3bar))+(C*B*F3bar))
F2=(eye(size(F3*C*B))-(F3*C*B))*F2bar
F1=(eye(size(F3*C*B))-(F3*C*B))*F1bar
Johan Löfberg
Oct 6, 2018, 11:32:35 AM10/6/18
to YALMIP
optimal -0.04, solution strictly feasible
F3 =
550.1115 294.9079
-26.4204 50.5502
F2 =
127.4715 63.2173
5.6316 2.9827
F1 =
419.6013 45.4063
-1.7137 -4.7159
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