Iteration Complexity of a Proximal Augmented Lagrangian Method for Solving Nonconvex Composite Optimization Problems with Nonlinear Convex Constraints

• 成果类型: Article
• 署名作者: Kong, Weiwei; Melo, Jefferson G.; Monteiro, Renato D. C.
• 署名单位: United States Department of Energy (DOE); Oak Ridge National Laboratory; Universidade Federal de Goias; University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1301
• 发表日期: 2023
• 页码: 1066-1094
• 关键词: point method; algorithm

摘要

This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving constrained nonconvex composite optimization problems, where the constraints are smooth and convex with respect to the order given by a closed convex cone. Each NL-IAPIAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient method followed by a Lagrange multiplier update. Under some mild assumptions, a complexity bound for NL-IAPIAL to obtain an approximate stationary solution of the problem is also derived. Numerical experiments are also given to illustrate the computational efficiency of the proposed method.