Exploiting Structure in Derivative-Free Composite Nonsmooth Optimization

Abstract: We present a pair of new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some algebraically specified (glass-box) mapping of a vector of outputs from a computationally expensive (black-box) function. This problem class covers many interesting problems from a wide range of applications relevant to the Department of Energy Office of Science, and has motivated a lot of work by myself and Jeff Larson (ANL/MCS). We provide rigorous convergence analysis and guarantees, and test the implementations on synthetic problems. For this particular presentation, I will also provide an introduction to the larger field of (model-based) black-box optimization.