Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension increases. Recent advances in developing randomized derivative-free techniques have tackled this issue by working in low-dimensional subspaces that are … Read more
Derivative-free algorithms seek the minimum value of a given objective function without using any derivative information. The performance of these methods often worsen as the dimension increases, a phenomenon predicted by their worst-case complexity guarantees. Nevertheless, recent algorithmic proposals have shown that incorporating randomization into otherwise deterministic frameworks could alleviate this effect for direct-search methods. … Read more
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 a sequential or simultaneous manner, the high- dimensional original problem into low-dimensional subproblems that can then be solved with any global, or even local, optimization solver. We estimate … Read more