题目：距离投影算子的Frechet 和Mordukovich 微分以及在随机不动点问题方面的应用
主讲人：李锦路
时间：2024-09-27 14:30
地点：教16208会议室
举办部门：数学与计算机学院数学系
讲座要点：
The theory of generalized differentiation in set-valued analysis is based on Mordukhovich derivative (Mordukhovich coderivative), which has been widely applied to optimization theory, equilibrium theory, variational analysis, with respect to set-valued mappings. In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for metric projection onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. This is considered as optimizing the metric projection with respect to covering values. We study three cases: closed balls in uniformly convex and uniformly smooth Banach spaces, closed and convex cylinders in lp and positive cones in Lp, for some p with 1 < p < . By Theorem 3.1 in [2] and as applications of covering constants obtained in this paper, we prove solvability of some stochastic fixed-point problems. We also provide three examples with specific solutions of stochastic fixed-point problems.
主讲人简介：
李锦路博士、教授，毕业于美国Wayne State University。在美国Wayne State University和Shawnee State University数学系从教三十多年，一直从事函数论、算子理论及不动点理论和应用的研究。近年来，致力于赋序集上的不动点理论和应用的研究，首次证明了链完备半序集上的集值映射不动点定理，并在赋序变分方程、具有半序效益函数的博弈中广义 Nash均衡点的存在性，以及一些积分方程的可解性等领域得到许多应用，解决了拓扑半序空间中存在交替的闭拓扑算子和可传递算子不稳定的长期未解决的问题，在国际专业期刊上发表论文 110余篇。