文献类型：期刊文献

英文题名：Mathematical programs with complementarity constraints and a non-Lipschitz objective: optimality and approximation

作者：Guo, Lei[1];Chen, Xiaojun[2]

机构：[1]East China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

年份：2021

卷号：185

期号：1-2

起止页码：455

外文期刊名：MATHEMATICAL PROGRAMMING

收录：;EI(收录号：20194407594649);WOS:【SCI-EXPANDED(收录号:WOS:000608923300014)】；

语种：英文

外文关键词：Mathematical program with complementarity constraints; Non-Lipschitz continuity; Sparse solution; Optimality condition; Approximation method

摘要：We consider a class of mathematical programs with complementarity constraints (MPCC) where the objective function involves a non-Lipschitz sparsity-inducing term. Due to the existence of the non-Lipschitz term, existing constraint qualifications for locally Lipschitz MPCC cannot ensure that necessary optimality conditions hold at a local minimizer. In this paper, we present necessary optimality conditions and MPCC-tailored qualifications for the non-Lipschitz MPCC. The proposed qualifications are related to the constraints and the non-Lipschitz term, which ensure that local minimizers satisfy these necessary optimality conditions. Moreover, we present an approximation method for solving the non-Lipschitz MPCC and establish its convergence. Finally, we use numerical examples of sparse solutions of linear complementarity problems and the second-best road pricing problem in transportation science to illustrate the effectiveness of our approximation method for solving the non-Lipschitz MPCC.