getting error: no suitable solver

[Sahere Rahimi]

Hi every one

I have a problem, i hope you help me

I want to solve a function which is attached, I used random input data to solve it,

the code which used in MATLAB is as following:

s1=rand(3,3);%%% equal to Sw'

s2=rand(3,3);%%% equal to Sw

beta=sdpvar(3,1);

B=sdpvar(3,3);

F=[beta(:)>=0,B-beta*beta'>=0,trace(s2*B)==1];  %%% beta(:)>=0: equal to em'beta>=0

optimize(F,trace(s1*B));

but my output is as following:

ans = 

    solvertime: 0

          info: 'No suitable solver'

       problem: -2

    yalmiptime: 0.1720

what is wrong?

please help me about this

[Johan Löfberg]

You've set up a quadratic semidefinite problem, and don't have any solver for that. However, you quadratic semidefinite constraint is easily converted to an LMI, just as described in the attached picture.

[Sahere Rahimi]

Thank you, do you mean that i cannot solve it by YALMIP? 

sorry, i am beginner about optimization toolbox, can you explain me more what should i do? 

About LMI, do you means that i should write the constraint as its matrix form?

can you give me the correct code to solve the problem?

[Sahere Rahimi]

I used constraint as following:

F=[beta(:)>=0,[1 beta';beta B]>=0,(trace(s2*B))==1];

now the output is as following:

    yalmiptime: 0.1708

    solvertime: 0.2502

          info: 'Unbounded objective function (SDPT3-4)'

       problem: 2

what dose it mean? what should i do?

[Johan Löfberg]

Not in the current form as it is a nonlinear SDP, but if you simply implement it as it is implemented in the .jpg (where a Schur complement has been applied), YALMIP + any standard SDP solver will solve it. It is a very easy problem

[Sahere Rahimi]

Thank you, I am so sorry asking many questions.

I used its Schur complement as following:

F=[beta(:)>=0,[1 beta';beta B]>=0,(trace(s2*B))==1];

after running ' optimize(F,trace(s1*B)) '  the output is as following:

    yalmiptime: 0.1708

    solvertime: 0.2502

          info: 'Unbounded objective function (SDPT3-4)'

       problem: 2

is it correct? i used following:

>> value(beta)

ans =

   1.0e-04 *

    0.5102

    0.5525

    0.5557

I think the value of beta is so small

[Johan Löfberg]

https://yalmip.github.io/debuggingunbounded/

[Sahere Rahimi]

I test it step by step:

1--------------> 

F=[beta(:)>=0,[1 beta';beta B]>=0,(trace(s2*B))==1];

optimize(F)

ans = 

    yalmiptime: 0.1756

    solvertime: 0.2924

          info: 'Lack of progress (SDPT3-4)'

       problem: 5

2----------------->

F=[0<=beta(:)<=1000,[1 beta';beta B]>=0,(trace(s2*B))==1];

optimize(F,trace(s1*B))

ans = 

    yalmiptime: 0.1801

    solvertime: 0.3039

          info: 'Unbounded objective function (SDPT3-4)'

       problem: 2

3------------------->

is numerical data poor?

[Johan Löfberg]

Looking closer, your model is theoretically bounded when you add bounds on beta, hence the problem is in your data as it still complains. Bad scaling etc

[Johan Löfberg]

Wrong by me. It is not necessarily bounded, Hence, either bad data, or simply unbounded by construction, i.e. flawed problem formulation. Add a bound on elements of B, and then look at how the solution of B evolves as you increase that bound, should reveal to you if it smells unbounded

[Sahere Rahimi]

I made input data (s1,s2) by "rand" in MATLAB.

I  added  a bound on B as following:

>> F=[0<=beta(:),0<[1 beta';beta B],B<10,(trace(s2*B))==1];

answer:

ans = 

    yalmiptime: 0.1701

    solvertime: 0.5499

          info: 'Numerical problems (SDPT3-4)'

       problem: 4

again, change the bound:

>> F=[0<=beta(:),[1 beta';beta B]>=0,B<1000,(trace(s2*B))==1];

ans = 

    yalmiptime: 0.1696

    solvertime: 0.7034

          info: 'Numerical problems (SDPT3-4)'

       problem: 4

,, I added the bound as following:

>> F=[0<=beta(:)<1000,0<[1 beta';beta B]<10000,(trace(s2*B))==1];

ans = 

    yalmiptime: 0.1751

    solvertime: 0.9639

          info: 'Infeasible problem (SDPT3-4)'

       problem: 1

>> F=[0<=beta(:)<1000,0<[1 beta';beta B]<100,(trace(s2*B))==1];

ans = 

    yalmiptime: 0.1629

    solvertime: 0.2891

          info: 'Infeasible problem (SDPT3-4)'

       problem: 1

By adding new bound , still there is problem

I am confused.

[Johan Löfberg]

Just random data is generically unbounded, so it makes no sense to test those models

[Johan Löfberg]

and I hope you realize that B<10 means B<ones(n)*10, which means you're saying the matrix largest eigenvalue is 0 (since ones(n) is singular), which causes issues as you said it is psd.

BTW, < is not supported. YALMIP screams at you about this

[Sahere Rahimi]

Thank you,

first, I should calculate s1 and s2 which are two graphs, after that i will solve the function.

calculation of these graphs take some hours, after that I will give you the results

Best regards