文献类型：期刊文献

英文题名：GLOBAL CONVERGENCE OF AUGMENTED LAGRANGIAN METHOD APPLIED TO MATHEMATICAL PROGRAM WITH SWITCHING CONSTRAINTS

作者：Guo, Lei[1];Li, Gao-Xi[2,3];Yang, Xinmin[4]

机构：[1]East China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Peoples R China;[3]Chongqing Technol & Business Univ, Sch Math & Stat, Chongqing 400067, Peoples R China;[4]Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

年份：2023

卷号：19

期号：6

起止页码：3868

外文期刊名：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

收录：;EI(收录号：20231513872252);WOS:【SCI-EXPANDED(收录号:WOS:000826351600001)】；

基金：The first author was supported in part by Natural Science Foundation of Shanghai(22ZR1415900), the National Natural Science Foundation of China(72131007), the Fundamental Research Funds for the Central Universities; The second author was supported in part by National Natural Science Foundation of China (11871383,11901068), the Project of National Center for Applied Mathematics(ncamc2021-msxm01); The third author was supported in part by Natural Science Foundation of Chongqing (cstc2019jcyj-zdxmX0016).

语种：英文

外文关键词：Mathematical program with switching constraints; either-or-constrained program; augmented Lagrangian method

摘要：The mathematical program with switching constraints (MPSC) is a kind of problems with disjunctive constraints. The existing convergence results cannot directly be applied to this kind of problem since the required constraint qualifications for ensuring the convergence are very likely to fail. In this paper, we apply the augmented Lagrangian method (ALM) to solve the MPSC and an application of the MPSC (i.e., the either-or-constrained program). We show that, under the MPSC relaxed constant positive linear dependent condition recently proposed in the literature, the feasible accumulation points of the iterates generated by the ALM are guaranteed to be strongly stationary if the multiplier sequence is bounded. When the multiplier sequence is unbounded, the feasible accumulation points are weakly stationary if MPSC linear independence constraint qualification holds. Some numerical experiments are conducted and compared with the recently proposed relaxation method. The numerical results demonstrate the effectiveness of the ALM and show that ALM can find better solutions than the relaxation method.