NonOpt: Nonconvex, Nonsmooth Optimizer

TL;DR

NonOpt addresses the challenge of minimizing locally Lipschitz, potentially nonconvex and nonsmooth objectives by combining gradient-sampling and proximal-bundle strategies. It employs quasi-Newton acceleration and solves per-iteration subproblems that are quadratic with linear equality and bound constraints, using specialized dual or interior-point solvers. A key contribution is the interior-point solver tailored to the QP subproblems arising in these methods, complementing an existing dual active-set approach and enabling efficiency on both small and large-scale problems, including inexact subproblem solutions. The framework is designed for extensibility with alternative search-direction and globalization strategies, and numerical results illustrate the method's speed and reliability on challenging problems.

Abstract

NonOpt, a C++ software package for minimizing locally Lipschitz objective functions, is presented. The software is intended primarily for minimizing objective functions that are nonconvex and/or nonsmooth. The package has implementations of two main algorithmic strategies: a gradient-sampling and a proximal-bundle method. Each algorithmic strategy can employ quasi-Newton techniques for accelerating convergence in practice. The main computational cost in each iteration is solving a subproblem with a quadratic objective function, a linear equality constraint, and bound constraints. The software contains dual active-set and interior-point subproblem solvers that are designed specifically for solving these subproblems efficiently. The results of numerical experiments with various test problems are provided to demonstrate the speed and reliability of the software.