报告一题目: Inexact proximal point method with a Bregman regularization for quasiconvex multiobjective optimization problems via limiting subdifferentials

内容摘要：In this talk, we investigate a class of unconstrained multiobjective optimization problems (abbreviated as, MPQs), where the components of the objective function are locally Lipschitz and quasiconvex. To solve MPQs, we introduce an inexact proximal point method with Bregman distances (abbreviated as, IPPMB) via Mordukhovich limiting subdifferentials. We establish the well-definedness of the sequence generated by the IPPMB algorithm. Based on two versions of error criteria, we introduce two variants of IPPMB, namely, IPPMB1 and IPPMB2. Moreover, we establish that the sequences generated by the IPPMB1 and IPPMB2 algorithms converge to the Pareto–Mordukhovich critical point of the problem MPQ. In addition, we derive that if the components of the objective function of MPQ are convex, then the sequences converge to the weak Pareto efficient solution of MPQ. Furthermore, we investigate the linear and superlinear convergence of the sequence generated by the IPPMB2 algorithm

报告二题目:Robust optimality and duality formultiobjective semi-infinite programming problems with equilibrium constraints under data uncertainty

内容摘要：In this talk, we discuss about a class of uncertain multiobjective semi-infinite programming problems with equilibrium constraints (abbreviated as UMSIPECs). We formulate the robust counterpart of UMSIPEC, that is, the robust multiobjective semi-infinite programming problems with equilibrium constraints (abbreviated as RMSIPEC). To establish the necessary criteria of local robust weak Pareto efficiency for RMSIPEC, we introduce the generalized standard Abadie constraint qualification (abbreviated as GS-ACQ) for RMSIPEC. Moreover, by employing the convexity assumptions, we deduce the sufficient criteria for robust weak Pareto efficiency for RMSIPEC. Furthermore, we formulate the Mond-Weir and Wolfe-type dual problems related to the problem RMSIPEC and derive weak as well as strong duality results that relate the primal problem RMSIPEC and the corresponding dual problems.

时 间：12月22日下午16:00，12月23日下午16:00；

报告地点：新民楼C408

专家简介：Balendu Bhooshan Upadhyay（中文名：巴伦杜·布尚·乌帕德亚伊），印度理工学院巴特那分校（印度巴特那理工）数学系助理教授。主要从事变分不等式、不动点理论及最优化领域的研究，特别在Hadamard流形上的多目标优化、半无限规划及非光滑优化等方面完成了一系列有意义的工作。近年来在Journal of Global Optimization、Journal of Optimization Theory and Applications、Journal of Computational and Applied Mathematics、Mathematics 等国际知名期刊上发表多篇学术论文。于贝拿勒斯印度教大学获得博士学位，并曾在该校从事博士后研究工作，此后先后任教于曼尼普尔国家技术学院及印度理工学院巴特那分校。