文献类型：期刊文献

英文题名：A New Augmented Lagrangian Method for MPCCs-Theoretical and Numerical Comparison with Existing Augmented Lagrangian Methods

作者：Guo, Lei[1];Deng, Zhibin[2]

机构：[1]East China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]Univ Chinese Acad Sci, Chinese Acad Sci, Sch Econ & Management, Key Lab Big Data Min & Knowledge Management, Beijing 100190, Peoples R China

年份：2022

卷号：47

期号：2

起止页码：1229

外文期刊名：MATHEMATICS OF OPERATIONS RESEARCH

收录：;EI(收录号：20222912373785);WOS:【SCI-EXPANDED(收录号:WOS:001125490900016)】；

基金：Guo received financial support from the National Natural Science Foundation of China [Grants 71632007, 72131007, and 11771287] and the Fundamental Research Funds for the Central Universities. Z. Deng received financial support from the National Natural Science Foundation of China [Grant 72171151].

语种：英文

外文关键词：mathematical program with complementarity constraints; augmented Lagrangian method; nonmonotone projected gradient method; M-stationarity

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.