Large scale nonlinear semidefinite optimization

Hi there,

I am trying to carry out a large scale nonlinear semidefinite optimization problem and am having trouble finding a solver that can handle the size of the task. I am currently using the PENLAB solver inside the YALMIP optimization environment, but my computer crashes (completely cuts out) after it has already spent hours trying to iterate to a solution.

The problem is an intermediate step in an estimation procedure i am carrying out in MATLAB, so it would be ideal if i could solve this part of the problem in MATLAB also. I was wondering if anyone could recommend any other solvers\programs\software that may be able to handle a large scale nonlinear semidefinite optimization problem?

I have not included technical details of the problem, but am happy to provide them if needed. In short i am minimizing the distance between the covariance matrices of observed data, and a theoretical covariance structure that comprises of certain parameters. The semidefinite constraints arise from the fact that the estimated parameters of the theoretical structure that minimize the distance between the two matrices have to be chosen such that the resultant matrix they make up is positive semidefinite.

Thanks in advance for any suggestions!

Mark

Answer 1

[Matt J]

You can specify a semi-definite constraint in FMINCON on a parametric matrix M(theta) by expanding the list of unknown variables theta to include an unknown matrix L. Then include the nonlinear constraint

M(theta)=L.'*L