勷勤数学•专家报告

题      目：Stability and scalarization for set optimization with Hausdorff continuity via general ordering sets

报  告  人： 彭再云 教授  (邀请人：陈艳男)

                                              云南师范大学

时      间： 9月20日  17：30-18:30

地     点：数科院东楼二楼会议室

报告人简介:

          彭再云，教授、博士生导师、省部级学术技术带头人、省部级创新研究群体带头人。云南师范大学数学优化理论及应用国际研究中心执行主任、云南省现代分析数学及其应用重点实验室副主任；中国运筹学会数学规划分会理事、中国运筹学会算法软件与应用分会理事、中国管理现代化研究会管理与决策科学专委会委员。研究方向为向量优化理论、算法及应用。在JOTA、JGO、SVVA、FSS、CNSNS等重要学术期刊发表论文100余篇，其中SCI检索论文80余篇(含top期刊和高被引、热点论文)。主持国家自科面上项目、青年项目、地区项目、外专项目及国家博士后基金特助项目（特助）各等省部级以上纵向科研项目20余项，担任著名优化期刊《Journal of Optimization Theory and Application》、《Optimization》的副主编。

摘      要：

           The aim of this paper is to investigate the scalarization and well-posedness for set optimization problems where the solution concept is given by the lower set less relation induced by general sets. First, we propose three kinds of well-posedness for set optimization problems via general sets and study their relationships. Moreover, some sufficient conditions for these kinds of well-posedness for set optimization problems via free-disposal set are obtained under the Hausdorff P-continuity of the objective mapping of the set optimization problem, rather than the continuity in the sense of Berge. By employing a nonlinear scalarization technique by means of the oriented distance function, corresponding scalar optimization problems are established, and the relationship between solutions of the set optimization problem where the solution concept is given by the lower set less relation induced by co-radiant sets and solutions of the corresponding scalarized problem is also discussed. Furthermore, we also give some characterization of well-posedness for set optimization problem through two scalar optimization problems. Some examples are given to illustrate the main results.

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