Abstract

The purpose of this paper is to establish a Fritz John type first order necessary condition for constrained nonlinear optimization problems in infinite dimensional spaces via the finite codimension condition. Different form the known constraint qualifications in infinite dimensional optimization theory, the finite codimension condition introduced in this paper is much easy to be verified. To illustrate this, some equivalent verification conditions for finite codimension condition are proposed. As applications, the first order necessary conditions for optimal control problems governed by various control systems are derived in a uniform way.

个人简介：张海森，四川师范大学数学科学学院教授，博士生导师。2014年6月博士毕业于四川大学，2016年10月至2017年10 月在法国巴黎第六大学做访问学者。现担任美国数学会《数学评论》评论员，中国运筹学会数学规划分会青年理事。2020年获第十七届霍英东教育基金会高等院校青年教师奖三等奖。主要研究领域为随机系统的控制理论，目前主持和参与国家自然科学基金项目5项，发表SCI学术论文12篇。部分研究成果发表在SIAM Review，Trans. American Math. Soc.，J. Differential Equations，SIAM J. Control Optim.等学术期刊上。