A New Augmented Lagrangian Method for MPCCs-Theoretical and Numerical Comparison with Existing Augmented Lagrangian Methods

• 成果类型: Article
• 署名作者: Guo, Lei; Deng, Zhibin
• 署名单位: East China University of Science & Technology; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1165
• 发表日期: 2022
• 页码: 1229-1246
• 关键词: mathematical programs; complementarity constraints; optimality conditions; convergence properties; regularization scheme; GLOBAL CONVERGENCE; elastic mode

摘要

We propose a new augmented Lagrangian (AL) method for solving the mathematical program with complementarity constraints (MPCC), where the complementarity constraints are left out of the AL function and treated directly. Two observations motivate us to propose this method: The AL subproblems are closer to the original problem in terms of the constraint structure; and the AL subproblems can be solved efficiently by a nonmonotone projected gradient method, in which we have closed-form solutions at each iteration. The former property helps us show that the proposed method converges globally to an M-stationary (better than C-stationary) point under MPCC relaxed constant positive linear dependence condition. Theoretical comparison with existing AL methods demonstrates that the proposed method is superior in terms of the quality of accumulation points and the strength of assumptions. Numerical comparison, based on problems in MacMPEC, validates the theoretical results.