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]East China Univ Sci & Technol, Sch Business, Shanghai 200237, Peoples R China;[2]Univ Victoria, Dept Math & Stat, Victoria, BC V8W 2Y2, Canada;[3]Southern Univ Sci & Technol, SUSTech Int Ctr Math, Natl Ctr Appl Math Shenzhen, Dept Math,Peng Cheng Lab, Shenzhen, Peoples R China

年份：2024

卷号：49

期号：1

起止页码：536

外文期刊名：MATHEMATICS OF OPERATIONS RESEARCH

收录：;EI(收录号：20241816019815);WOS:【SCI-EXPANDED(收录号:WOS:000974060000001)】；

语种：英文

外文关键词：sensitivity analysis; value function; Wolfe duality; nonconvex minimax problem; non-Lipschitz continuity; necessary optimality

摘要：In this paper, we perform a 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 Fre ' chet, 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 compares favorably with the first-order approach in that the necessary condition is sharper and the constraint qualification is weaker.