Jeffrey Larson : Expensive Derivative-Free Nonsmooth Composite Optimization

Posted by David Nicholls , part of the Analysis and Applied Mathematics Seminar.

At

Oct. 23, 2023, 4 p.m.

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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.