Convex hull of PSD matrices

bastpg

Hi,
I want to check if a given PSD matrix, say A, is contained in the convex hull of a set of PSD matrices, say Set={S_i, i:1..N}. In other word I want to check whether there exist real constants lambda_i such that:
1) sum_over_i{ lambda_i*S_i } - A >=0, where >=0 in this equation means that the matrix on the left is PSD;
2) sum_over_i{ lambda_i }=1
3) lambda_i>=0 for all i
Let me know if you know how to solve this pb...
Thanks,
Bastien