random subspaces

Direct search based on probabilistic descent in reduced spaces

  • Lindon Roberts
  • ClĂ©ment W. Royer
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    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

    Global optimization using random embeddings

  • Coralia Cartis
  • Estelle Massart
  • Adilet Otemissov
    • Categories Global Optimization, Nonlinear Optimization Tags , , , ,

    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