A Derivative-Free Method for Structured Optimization Problems

Structured optimization problems are ubiquitous in fields like data science and engineering. The goal structured is using a prescribed set of points, called atoms, to build up solution that minimizes or maximizes given function. In the present paper, we want minimize black-box function over convex hull problem can be used model number real-world applications. We focus on whose solutions sparse, i.e., obtained as proper combination just few atoms set, propose suitable derivative-free inner approximation approach nicely exploits structure problem. This enables us properly handle dimensionality issues usually connected with algorithms, thus getting method scales well terms both dimension atoms. analyze global convergence stationary points. Moreover, show that, under assumptions, proposed algorithm identifies specific subset zero weight final after finitely many iterations. Finally, report numerical results showing effectiveness method.