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We propose a multistart algorithm to identify all local minima of aconstrained, nonconvex stochastic optimization problem. The algorithm uniformlysamples points in the domain and then starts a local stochastic optimizationrun from any point that is the "probabilistically best" point in itsneighborhood. Under certain conditions, our algorithm is shown toasymptotically identify all local optima with high probability; this holds eventhough our algorithm is shown to almost surely start only finitely many localstochastic optimization runs. We demonstrate the performance of animplementation of our algorithm on nonconvex stochastic optimization problems,including identifying optimal variational parameters for the quantumapproximate optimization algorithm.

Multistart Algorithm for Identifying All Optima of Nonconvex Stochastic Functions