Subspace Modeling and Random Subspace Trust-region Methods in Derivative-free Optimization (1h)

Abstract

Derivative-free optimization (DFO) is essential for problems where derivatives are unavailable or expensive to compute, but its scalability is limited by the high cost of model construction in large dimensions. Subspace techniques address this challenge by building models and performing optimization in low-dimensional affine subspaces.  This talk presents a unified view of subspace modelling and methods for DFO.  We first establish theoretical connections between full-space and subspace linear and quadratic models and simplex derivatives, showing that they coincide on the underlying subspace and along orthogonal directions.  We then present random subspace trust-region methods that leverage these models, including frameworks with provable convergence and complexity guarantees for unconstrained and convex-constrained problems.

Yiwen Chen

PhD student in Mathematics

My research interests center on the theoretical foundations of derivative-free optimization, with a particular emphasis on model accuracy, complexity analysis, and randomized subspace methods for high-dimensional problems. I am also interested in discrete geometry and polytope theory.