Is it possible to set initial values for optimization variables in a SDP problem

[Boran Zhao]

Hi Johan, 

I am currently using Yalmip + LMI Lab to solve a BMI problem by iteratively solving a series of SDP problem. I know that you recommend other solvers like sedumi, sdpt3 and mosek instead of LMI Lab. However, for my problem, I found LMI Lab is more reliable than other SDP solvers, which often give infeasibility problem after several iterations or give results that do not make sense.  I already tried the techniques by adding the penalty term of optimization variables (like norm(X)) in the cost function to improve numerical property, but it could not completely solve the problem. 

Therefore, I have to use LMI Lab solver for my problem. I also need to use Yalmip to significantly simply the coding. Now the only problem is low efficiency that you mentioned. I am now thinking to set initial values for the optimization variables to reduce computational time. This is because for iterative solving of SDP problems that I used, the results from iteration k can be used as initial values for the iteration k+1.  If I use LMI Lab separately, it is easy to set initial values by giving xinit in [copt,xopt] = mincx(lmisys,c,options,xinit,target).I was wondering whether it is possible for me to set initial values in Yalmip for LMI Lab solver with minimal coding. ( I assume this cannot be directly done currently)

Thanks a lot. 

Regards

Boran

[Johan Löfberg]

Not supported for lmilab.

These IP-solvers typically don't benefit much from an initial guess though, as the initial centering of the problem will be wrong, and time will be spent on getting lined up on the central path again etc.