林贵华(上海大学 教授)

戴彧虹 研究员

Solving Bilevel Programs Based on Lower-level Duality

10月19日 19:30-20:30, 腾讯会议：510-178-417

In this talk, we focus on bilevel programs, which have many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform bilevel programs into single-level optimization problems. The most popular approach is to replace the lower-level programs by their KKT conditions and then bilevel programs can be reformulated as mathematical programs with equilibrium constraints (MPEC for short). However, since MPECs do not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. Recently, we apply the lower-level Wolfe duality and the lower-level Mond-Weir duality to present two new single-level reformulations for bilevel programs. We show through examples that, unlike the MPEC reformulation, the new reformulations may satisfy the Mangasarian-Fromovitz constraint qualification at their feasible points. We investigate their properties and the relations with the MPEC reformulation. We further propose some relaxation methods and numerical experiments indicate that, although solving the new reformulations directly does not perform very well in our tests, the relaxation methods are more efficient than the MPEC approach.

报告人简介：林贵华,2004年博士毕业于日本京都大学，现任上海大学管理学院教授、博导、人怀学者，上海领军人才，入选辽宁省百千万人才工程。研究兴趣主要是与均衡相关的各种最优化问题及其在管理科学中的应用，在Mathematical Programming、SIAM Journal on Optimization、Mathematics of Computation、Automatica等国际知名期刊发表学术论文100余篇。主持国家自然科学基金项目4项、国家自科重点项目子课题2项、省部级项目6项。现任中国运筹学会理事、上海运筹学会理事、经济数学与管理数学分会常务理事等，《Pacific Journal of Optimization》、《运筹与管理》编委。所指导研究生获得国家级人才2人、省部级人才3人。