Solver not applicable issue in logdet maximization problem

[Shaik]

Dear Johan,

I am trying to solve the logdet maximization problem that maximize the region of applicability under some LMI constraints. I am getting an error 'solver not applicable' with sdpt3. If I dont use sdpt3, it shows 'no solver found'.

 Is it problem with solver?? The code is exactly as given below here.

A=[0.4 0.05;0.7 1.1]; Ab1=[0.09 0.03;0.03 0.09]; Ab2=[0.2 -0.04;-0.04 0.1]; 

B=[0.1 0.8]'; Bb1=[0.02 -0.01]'; Bb2=[-0.01 0.03]'; ub=0.3; p=0.9;

r=sqrt(chi2inv(0.9,1));

P = sdpvar(6,6,'symmetric');% Here P actually stands for inv(Cap P)

sdpvar ld;

F=[P>=0]; F=[F,0<=ld<=1]; % Constraints on P, lambda

%

K=[-0.2298   -0.5112]; 

Tx=[eye(2);zeros(4,2)]; % Tau_x

Psi= [A+B*K      B*[1 0 0 0];

      zeros(4,2) [0 1 0 0;0 0 1 0;0 0 0 1;0 0 0 0]];

Psib1= [Ab1+Bb1*K    Bb1*[1 0 0 0];

        zeros(4,6)];

Psib2= [Ab2+Bb2*K    Bb2*[1 0 0 0];

        zeros(4,6)];

% constraint in (36)

lmi1=[ub^2 [K 1 0 0 0]*P;

      ([K 1 0 0 0]*P)' P];

lmi2=[Tx'*P*Tx                      (Tx'*Psi*P)         Tx'*[Psib1*P Psib2*P];

     (Tx'*Psi*P)'                   (1-ld)*P           zeros(6,12);

     (Tx'*[Psib1*P Psib2*P])'       zeros(12,6)          [(ld/r^2)*P zeros(6);zeros(6) (ld/r^2)*P]];

  

F=[F, lmi1>=0]; F=[F, lmi2>=0];

optimize(F,-logdet(Tx'*P*Tx),sdpsettings('solver','sdpt3')) %maximize the logdet in (36) subject to (12), (16)

Px= inv(Tx'*value(P)*Tx)

Lambda = value(ld)

[Johan Löfberg]

You have a BMI as you multiply (1-ld)*P

+++++++++++++++++++++++++++++++++++++++++++++
|   ID|                           Constraint|
+++++++++++++++++++++++++++++++++++++++++++++
|   #1|                Matrix inequality 6x6|
|   #2|          Element-wise inequality 2x1|
|   #3|                Matrix inequality 7x7|
|   #4|   Matrix inequality (bilinear) 20x20|
+++++++++++++++++++++++++++++++++++++++++++++

You have to perform a bisection over ld

[Shaik]

Oh I forgot to notice this BMI!!

Thanks for the information.

[Mark L. Stone]

Or install Penlab?