讲座题目：Variational Analysis of Solution Mappings in Multi-objective Optimization
This presentation will focus on properties of solution sets in multi-objective optimization. Specifically, we will discuss recession properties of efficient and properly efficient solution sets as well as various implications based on these properties. We will also show that, for a large class of multi-objective optimization problems including polynomial optimization problems, any efficient solution possesses certain enhanced regularity property which has not been detected before. If time permits, we will report recent joint work on substantial efficiency and its applications.
讲座题目：Level-set Based Error Bounds： Theory and Applications to Convergence Rate Analysis of Minimization Algorithms
In this presentation, we will examine a number of level-set based error bounds and their inner-connections as well as their relationships to other types of error bounds. This viewpoint provides a fresh perspective that allows us to explore many known sufficient conditions for linear convergence of minimization algorithms including various first-order methods. Along the way, we are able to derive a number of verifiable conditions for level-set error bounds to hold, and obtain/reproduce linear convergence of many first-order methods. Part of this presentation is based on joint work with Daoli Zhu of Shanghai Jiao Tong University.
Sien Deng, 美籍华人，此刻是美国北伊利诺伊大学（Northern Illinois University）应用数学系传授，Deng传授在数学规划领域有着很深的造诣，目前在优化方向的顶级期刊《Mathematical Programming》、《Siam Journal on Optimization》和《Siam Journal on Control and Optimization》等期刊上发表了许多有影响力的学术性文章。