Optimization problems for elastic contact models with unilateral constraints

报告人简介：电子科技大学数学科学学院教授，博士生导师。主要从事变分不等式、半变分不等式、最优化理论及其在工程、力学以及交通科学中的应用等方面的研究。在《TRB》、《TRE》、《JOGO》、《JOTA》等运筹学、交通领域学术刊物上发表论文多篇；主持国家自然科学基金面上项目、青年基金项目,中国博士后科学基金特别资助项目等国家级、省部级科研项目。现任美国《Mathematical Reviews》的评论员、德国《数学文摘》评论员、中国运筹学会理事、中国运筹学会数学规划分会青年理事、四川省数学会理事；入选四川省第十批学术带头人后备人选。

报告内容：The aim of this talk is to provide some results in the study of an abstract optimization problem in reflexive Banach spaces and to illustrate their use in the analysis and control of static contact problems with elastic materials. We start with a simple model problem which describes the equilibrium of an elastic body in unilateral contact with a foundation. We derive a variational formulation of the model which is in the form of minimization problem for the stress field. Then we introduce the abstract optimization problem for which we prove existence, uniqueness and convergence results. The proofs are based on arguments of lower semicontinuity, monotonicity, convexity, compactness and Mosco convergence. Finally, we use these abstract results to deduce both the unique solvability of the contact model as well as the existence and the convergence of the optimal pairs for an associated optimal control problem.