I've been using YALMIP with SeDuMi to solve a feasibility semidefinite program, that is, I want to find a feasible point in a set of the form $$F=\{S\in Sym_d(\mathbb{R}) : ||h(S)||\leq C(S_0), S\succeq 0\},$$ where $C(S_0)$ is a positive real and $h$ is an array of linear functions of $S$ (something like $h_j(S)=trace(A_j^tS)$, where $A_j$ are real matrices) and $Sym_d(\mathbb{R})$ is the set of all $d\times d$ symmetric matrices over $\mathbb{R}$.
So far, YALMIP seems to handle the norm constraint (and everything else) nicely, but I do have an initial guess $S_0$ (not necessarily feasible) and I would like to use this information somehow. Is this possible?
Something like minimizing $||S-S_0||$ subject to $S\in F$ makes sense to me, but it doesn't seem to work (the package is capable of solving it, but the solution is not as good as I expected).
Any suggestions would be much appreciated. Thank you in advance.