文献类型：期刊文献

英文题名：Sensitivity analysis of the maximal value function with applications in nonconvex minimax programs

作者：Guo, Lei[1]; Ye, Jane J.[2]; Zhang, Jin[3]

机构：[1] School of Business, East China University of Science and Technology, Shanghai, 200237, China; [2] Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada; [3] Department of Mathematics, SUSTech International Center for Mathematics, Southern University of Science and Technology, National Center for Applied Mathematics Shenzhen, Peng Cheng Laboratory, Guangdong, Shenzhen, China

年份：2023

外文期刊名：arXiv

收录：EI(收录号：20230083391)

语种：英文

外文关键词：Application programs - Optimization

摘要：In this paper, we perform sensitivity analysis for the maximal value function which is the optimal value function for a parametric maximization problem. Our aim is to study various subdifferentials for the maximal value function. We obtain upper estimates of Fréchet, limiting, and horizon subdifferentials of the maximal value function by using some sensitivity analysis techniques sophisticatedly. The derived upper estimates depend only on the union of all solutions and not on its convex hull or only one solution from the solution set. Finally, we apply the derived results to develop some new necessary optimality conditions for nonconvex minimax problems. In the nonconvex-concave setting, our Wolfe duality approach compare favourably with the first order approach in that the necessary condition is sharper and the constraint qualification is weaker.MSC Codes 90C30, 90C31, 90C47 ? 2023, CC BY.