What algorithm does CVX implement when solving the “feasibility problem” for SDPs? That is, I have the feasible set for an SDP, and CVX produces a feasible solution. Is there a good reference??
On a deeper level; my (preliminary) understanding is that, unlike for LPs and the simplex, the “presolving step” of finding a feasible solution for an SDP is not an SDP. This is all the more confusing to me because all the hype about semi-algebraic optimization arises from the observation that nonnegativity certificates can be phrased as SDP feasibility problems, for which we have “fast” algorithms…yet most algorithms for SDP problems start by assuming a feasible solution (at least a feasible psd matrix as part of the initial solution…). Then one wonders: what are the good references detailing algorithms for finding a feasible point (psd matrix) given PSD program constraints?