Mathematical Programs with Complementarity Constraints and a Non-Lipschitz Objective: Optimality and Approximation
报告人:郭磊副教授,华东理工大学 时间:2019年12月13日16:00
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.
报告人简介:郭磊博士,现为华东理工大学商学院副教授、特聘研究员。运筹学会数学规划分会青年理事,经济数学与管理数学分会理事。2013年在大连理工大学获得博士学位,2014-2015年在加拿大维多利亚大学做博士后研究,2015-2018年就职于上海交通大学任助理教授、副教授。研究兴趣包括最优化理论和方法、供应链管理、共享出行管理优化等,共发表SCI期刊论文18篇,其中在最优化领域国际顶级期刊Mathematical Programming、SIAM系列期刊、Mathematics of Operations Research共发表论文8篇。