Lmilab is successful, but mosek is infeasible, why

[Zihao Cheng]

close all;%%

clear all;%%%

M=10;m=1;l=3;g=10;

A=[0 1 0 0; 0 0 -m*g/M 0; 0 0 0 1; 0 0 g/l 0];

B=[0; 1/M; 0; -1/(M*l)];

Bw=ones(4,1);

C=Bw';

D=0.1;

det=0.1; p=0.53; r=200; td=0.16;

X=sdpvar(4,4);

Q_=sdpvar(4,4);

R_=sdpvar(4,4);

Omg_=sdpvar(4,4);

N_=sdpvar(16,4);

M_=sdpvar(16,4);

Y=sdpvar(1,4);

F_11a=[A*X+X*A'+Q_, B*Y, zeros(4), B*Y;

    Y'*B', det*Omg_, zeros(4), zeros(4);

    zeros(4), zeros(4), -Q_, B*Y;

    Y'*B', zeros(4), zeros(4), -Omg_];

F_11b=[-N_, N_-M_, M_, zeros(16,4)];

F_21a=sqrt(td)*N_';F_21b=sqrt(td)*M_';

F_31=[Bw', zeros(1,4), zeros(1,4), zeros(1,4)];

F_41=[sqrt(td)*A*X, sqrt(td)*B*Y,  zeros(4), sqrt(td)*B*Y];

F_51=[C*X, D*Y, zeros(1,4), D*Y];

F1=[F_11a+F_11b+F_11b', F_21a', F_31', F_41', F_51';

    F_21a, -R_, zeros(4,1), zeros(4), zeros(4,1);

    F_31, zeros(1,4), -r^2, sqrt(td)*Bw', zeros(1);

    F_41, zeros(4), sqrt(td)*Bw, p^2*R_-2*p*X, zeros(4,1);

    F_51, zeros(1,4), zeros(1), zeros(1,4), -1];

F2=[F_11a+F_11b+F_11b', F_21b', F_31', F_41', F_51';

    F_21b, -R_, zeros(4,1), zeros(4), zeros(4,1);

    F_31, zeros(1,4), -r^2, sqrt(td)*Bw', zeros(1);

    F_41, zeros(4), sqrt(td)*Bw, p^2*R_-2*p*X, zeros(4,1);

    F_51, zeros(1,4), zeros(1), zeros(1,4), -1];

F=(X>=0)+(Q_>=0)+(R_>=0)+(Omg_>=0)+(F1<=0)+(F2<=0);

ops=sdpsettings('solver','lmilab');

optimize(F,[],ops)

%optimize(F)%mosek

check(F)

X=value(X);

Y=value(Y);

Q_=value(Q_)

R_=value(R_);

N_=value(N_);

M_=value(M_);

Omg_=value(Omg_)

Lm2=[F_11a+F_11b+F_11b', F_21a', F_31', F_41', F_51';

    F_21a, -R_, zeros(4,1), zeros(4), zeros(4,1);

    F_31, zeros(1,4), -r^2, sqrt(td)*Bw', zeros(1);

    F_41, zeros(4), sqrt(td)*Bw, p^2*R_-2*p*X, zeros(4,1);

    F_51, zeros(1,4), zeros(1), zeros(1,4), -1]

K=Y*inv(X)

Omg=inv(X)*Omg_*inv(X)

The above theorem is the objective of my simulation. I wander that there exist  simultaniously \tilde{Q} and -\tilde{Q}, \tilde{\Omega} and -\delta \tilde{\Omega}  as diagnal terms. I think it is not feasible. However, it is feasible by using  solver lmilab, but infeasible by using solve mosek. As Johan Lofberg said, mosek is more fast and robust in YALMIP. I need help. 

[Johan Löfberg]

I don't think you meant F1 and F2 to be non-symmetric (i.e. not LMI constraints)

>> F

++++++++++++++++++++++++++++++++++++++++

|   ID|                      Constraint|

++++++++++++++++++++++++++++++++++++++++

|   #1|           Matrix inequality 4x4|

|   #2|           Matrix inequality 4x4|

|   #3|           Matrix inequality 4x4|

|   #4|           Matrix inequality 4x4|

|   #5|   Element-wise inequality 520x1|

|   #6|   Element-wise inequality 520x1|

++++++++++++++++++++++++++++++++++++++++

and if you use lmilab on an infeasible problem, it will not tell yalmip (and thus you) if it is infeasible, that is one of the main not to use lmilab

[Zihao Cheng]

Dear Johan,

     Thank you for your reply firstly. Should i understand your means that it does not make sense that it uses LMILAB with YALMIP. Even though the results is positive as following, your suggestion is that never use LMILAB and  ignore its results. right?     

%%%%%

yalmiptime: 4.0363

    solvertime: 0.1917

          info: 'Successfully solved (LMILAB)'

       problem: 0

 Through it displays successful, this "success" represents nothing.  

[Johan Löfberg]

https://yalmip.github.io/solver/lmilab/