报告人：张进博士

报告题目：双层规划最优性条件研究及其在委托-代理模型中的应用

摘要：Ye and Zhu in 2010 combined the classical first-order and the value function approaches to derive new necessary optimality conditions for the bilevel programming problem (BLPP). The partial calmness is an important condition which ensures that a local optimal solution of BLPP is a local optimal solution of a partially penalized problem, and hence necessary optimality conditions can be derived under a weaker constraint qualification. In this talk, we first analyse the partial calmness for the combined approach from a generic point of view. Our result states that the partial calmness for the combined approach is generic (in sense of Whitney C^3-topology) for an important setting with applications in principal-agent models. Moreover we derive optimality conditions for the combined approach for the generic case without any extra constraint qualifications. We also propose a combined approach with second-order optimality conditions of the lower level problem to study optimality conditions for BLPP. We show that when all known approaches fail, adding the second-order optimality condition as a constraint makes the corresponding partial calmness easier to hold. We also give some discussions on optimality conditions and advantages and disadvantages of the combined approaches with the first-order and the second-order information.

报告人简介：张进博士2007、2010年本科、硕士毕业于大连理工大学，2014年博士毕业于加拿大维多利亚大学。2015至2018年间任职香港浸会大学数学系，2019年初加入南方科技大学数学系。张进博士一直致力于最优化理论和应用研究，主持多项国家级基金项目，代表性成果发表在MP、SIOPT、SINUM、JMLR、ICML、NeurIPS等有影响力的应用数学、机器学习期刊与会议上。

报告时间：2021年11月25号下午15:30-17:30

报告形式：腾讯会议；会议号：793234821