勷勤数学•专家报告

题      目：A new sequential optimality condition and its algorithmic consequences for bilevel optimization problems

报  告  人： 张进 教授  (邀请人：王晓宙)

                                              南方科技大学

时      间： 9月20日  14：30-15:30

地     点：数科院东楼二楼会议室

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。致力于最优化理论和应用研究，代表性成果发表在Math Program、SIAM J Optim、Math Oper Res、SIAM J Numer Anal、Informs. J. Comput、J Mach Learn Res、IEEE Trans Pattern Anal Mach Intell，以及ICML、NeurIPS、ICLR等有重要影响力的最优化、计算数学、机器学习期刊与会议上。研究成果获得中国运筹学会青年科技奖、广东省青年科技创新奖。

摘      要：

           This paper studies constrained bilevel optimization problems for which the lower-level problem may fail to satisfy strong constraint qualifications, such as the Mangasarian--Fromovitz Constraint Qualification (MFCQ). We introduce BLP-AKKT, a new sequential optimality condition formulated directly for constrained bilevel optimization rather than through an MPEC reformulation. Under the Polyak--Lojasiewicz constraint qualification (PLCQ) imposed on the lower-level problem, we establish the necessity of BLP-AKKT for local optimality. Building on this condition, we develop a modular single-loop algorithmic framework and prove that every feasible accumulation point generated by algorithms within this framework satisfies BLP-AKKT. Using the AKKT residual as a stationarity measure, we further derive convergence rate guarantees for two specific instances: one based on gradient-descent updates and the other on a recursive momentum technique. Numerical experiments on synthetic instances and instances from the Bilevel Optimization LIBrary (BOLIB) demonstrate the effectiveness of the proposed algorithms compared with MPEC-based relaxation methods and value function-based methods.

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