Initial point exploitation for SDPs.

[Koto]

Hello.

My algorithm needs to solve this feasibility problem every iteration (there exists a solution) and I suspect that the loss of information about the previous value of S can lead to some sort of convergence issue.

This question was previously posted on Math Stackexchange and I just took a print of it and pasted here because I don't know if it is possible to insert Tex format in Google Groups.

[Johan Löfberg]

As explained here

https://yalmip.github.io/Initials

supplying initial guesses to standard convex conic solvers essentially never helps. They find the optimal solution easily without that, and typically you have no why of supplying a relevant primal-dual initial guess consistent with the internal machinery

However, in your descriptions, S0 has nothing to do with initial guess or anything. It sounds like you want to use the objective norm(S-S0) or something like that. If the optimal solution isn't as good as expected, then that objective simply doesn't communicate what you mean with "good".