CLARSTA: A random subspace trust-region algorithm for convex-constrained derivative-free optimization

Abstract

This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain accuracy of models and a certain quality of subspaces. For model accuracy, we define a new class of models that is only required to provide reasonable accuracy on the projection of the constraint set onto the subspace. We provide a new geometry measure to make these models easy to analyze, construct, and manage. For subspace quality, we use the concentration on the Grassmann manifold to provide a method to sample subspaces that preserve the first-order criticality measure by a certain percentage with a certain probability lower bound. Based on all these new theoretical results, we present an almost-sure global convergence and a worst-case complexity analysis of our algorithm. Numerical experiments on problems with dimensions up to 10000 demonstrate the reliable performance of our algorithm in high dimensions.

Yiwen Chen

PhD student in Mathematics

My research interests include derivative-free optimization, numerical optimization, and discrete geometry.