Smoothed analysis of the low-rank approach for smooth semidefinite programs

Inprior work, ithas been shown that, when the constraints on the factorized variable regularly define a smooth manifold, providedk is large enough, for almost all cost matrices, all second-order stationary points (SOSPs) are optimal. Importantly, in practice, one can only compute points which approximately satisfy necessary optimality conditions, leading tothequestion: aresuch points also approximately optimal?