报告地点：腾讯会议 205-493-851
邀请人：孙海琳教授
报告摘要：The partial calmness for the bilevel programming problem (BLPP) is an important condition which ensures that a local optimal solution of BLPP is a local optimal solution of a partially penalized problem where the lower-level optimality constraint is moved to the objective function and hence a weaker constraint qualification can be applied. In this paper, we propose a sufficient condition in the form of a partial error bound condition which guarantees the partial calmness condition. We analyze the partial calmness for the combined program based on the Bouligand (B) and the Fritz John (FJ) stationary conditions from a generic point of view. Our main result states that the partial error bound condition for the combined programs based on B and FJ conditions is generic for an important setting with applications in economics, and hence the partial calmness for the combined program is not a particularly stringent assumption. Moreover, we derive optimality conditions for the combined program for the generic case without any extra constraint qualifications and show the exact equivalence between our optimality condition and the one by Jongen and Shikhman [Math. Program., 136 (2012), pp. 65--89] given in implicit form. Our arguments are based on Jongen, Jonker, and Twilt's [Math. Program., 34 (1986), pp. 333--353] generic (five type) classification of the so-called generalized critical points for one-dimensional parametric optimization problems and Jongen and Shikhman's generic local reductions of BLPPs.
报告人简介：张进，南方科技大学数学系/深圳国家应用数学中心 副教授，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。从事最优化理论和应用研究，代表性成果发表在Math Program、SIAM J Optim、SIAM J Numer Anal、J Mach Learn Res、IEEE Trans Pattern Anal Mach Intell，以及ICML、NeurIPS 等最优化、计算数学、机器学习期刊与会议上。
