(1)Unified smoothing functions for absolute value equations;
(2) From symmetric cone optimization to non-symmetric cone optimization
报告人:陈界山 教授 (台湾师范大学)
报告摘要: (1) In this talk, we focus on the absolute value equation (AVE) and one of its extension, the absolute value equation associated with second order cone
(SOCAVE). For each equation, we propose unified smoothing functions that
can work along with smoothing-type algorithm. Some discovery based on
numerical comparisons is very interesting which may suggest a good choice
of smoothing function for the other contexts.
(2) It iswell known that Euclidean Jordan algebra is a unified framework for symmetric cone programs, including positive semidefinite programs and second-order cone programs. Unlike symmetric cone programs, there is no unified analysis technique to deal with nonsymmetric cone programs. Nonetheless, there are several common concepts when dealing with generalconic optimization. More specifically, we believe that spectral decomposition associated with cones, nonsmooth analysis regarding cone-functions, projections onto cones, and cone-convexity are the bridges between symmetric cone programs and nonsymmetric cone programs. Hence, this talk is devoted to looking into the first three items in the setting of nonsymmetriccones. The importance of cone-convexity is recognized in the literature so that it is not discussed here. All results presented in this paper are very crucial to subsequent study about the optimization problems associated with nonsymmetric cones.
报告人简介: 台湾师范大学数学系教授，博士生导师。2004年于美国华盛顿大学获得博士学位。曾访问英国南安普敦大学、德国符兹堡大学和美国华盛顿大学等。研究方向主要为，最优化理论与应用、非光滑分析和运筹学。目前已经发表SCI论文98篇。任Taiwanese Journal of Mathematics、Communications in Optimization Theory、Linear and Nonlinear Analysis、Journal of Nonlinear and Convex Analysis、Pacific Journal of Optimization、Mathematical Problems in Engineering、The Scientific World Journal - Mathematical Analysis等国际有影响力期刊的编委。现为台湾师范大学特聘教授和奖励特殊优秀人才。