## Analysis and Applied Mathematics Seminar

Jeffrey Larson

Mathematics & Computer Science, Argonne National Laboratory

Expensive Derivative-Free Nonsmooth Composite Optimization

**Abstract:**We present new methods for solving a broad class of bound-constrained smooth and nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive function. We provide accompanying implementations of these methods: in particular, a novel manifold sampling algorithm with subproblems that are in a sense primal versions of the dual problems solved by previous manifold sampling methods and a method that employs more difficult optimization subproblems. For these two methods, we provide rigorous convergence analysis and guarantees. We demonstrate extensive testing of these methods. Open-source implementations of these methods are available.

Monday October 23, 2023 at 4:00 PM in 636 SEO