Global optimization using random embeddings

Abstract We propose a random-subspace algorithmic framework for global optimization of Lipschitz-continuous objectives, and analyse its convergence using novel tools from conic integral geometry. X-REGO randomly projects, in sequential or simultaneous manner, the high-dimensional original problem into low-dimensional subproblems that can then be solved with any global, even local, solver. estimate probability randomly-embedded subproblem shares (approximately) same optimum as problem. This success is used to show almost sure an approximate solution problem, under weak assumptions on (having strictly feasible solution) solver (guaranteed find reduced sufficiently high probability). In particular case unconstrained objectives low effective dimension, we variant explores random subspaces increasing dimension until finding leading globally converging after finite number embeddings, proportional dimension. numerically this efficiently finds both minimizer