一、报告题目：A novel approach for bilevel programs based on Wolfe duality
二、报告人：林贵华教授-上海大学
三、报告时间：2022年4月21日星期四上午10:00
四、报告平台：腾讯会议
会议ID：597-282-066
五、摘要：
In this talk, we focus on a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be reformulated as a mathematical program with equilibrium constraints (MPEC for short). However, since the MPEC does not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. In this paper, we apply the Wolfe duality to show that, under very mild conditions, the bilevel program is equivalent to a new single-level reformulation (WDP for short) in the globally and locally optimal sense. We give an example to show that, unlike the MPEC reformulation, WDP may satisfy the Mangasarian-Fromovitz constraint qualification at its feasible points. We give some properties of the WDP reformulation and the relations between the WDP and MPEC reformulations. We further propose a relaxation method for solving WDP and investigate its limiting behavior. Comprehensive numerical experiments indicate that, although solving WDP directly does not perform very well in our tests, the relaxation method based on the WDP reformulation is quite efficient.
六、报告人简介：
林贵华，博士，教授，博士生导师，中国运筹学会理事，中国运筹学会数学优化分会理事，辽宁省百千万人才工程人选，现任上海大学管理科学与工程系主任。2004年博士毕业于日本京都大学。曾多次访问香港理工大学、香港浸会大学、加拿大维多利亚大学、英国南安普顿大学、日本弘前大学等。研究方向为均衡优化、供应链管理、工程管理、项目管理等。已在Mathematical Programming、SIAM Journal on Optimization、European Journal of Operational Research等国际期刊上发表学术论文90余篇。主持国家自然科学基金面上项目4项、国家自然科学基金重点项目子课题2项、省部级项目5项。
