基于凸化集的具有均衡约束的非光滑半无限规划对偶理论研究  

Duality for Nonsmooth Semi-infinite Programming with Equilibrium Constraints,Using Convexificators

作　　者：范红莲 苏珂[1,2] FAN Honglian;SU Ke(College of Mathematics and Information Science,Hebei University,Baoding 071002,China;Hebei Key Laboratory of Machine Learning and Computational Intelligence,Baoding 071002,China)

机构地区：[1]河北大学数学与信息科学学院,河北保定071002 [2]河北省机器学习与计算智能重点实验室,河北保定071002

出　　处：《应用数学》2025年第2期565-573,共9页Mathematica Applicata

基　　金：河北省自然科学基金(A2022201002)。

摘　　要：本文研究具有均衡约束的非光滑半无限规划问题的对偶性质,利用凸化集,对具有均衡约束的非光滑半无限规划问题提出其混合对偶模型.与传统对偶理论中的凸性不同,本文考虑了在凸算子下的∂*-凸和∂*-不变凸假设,并分别建立了具有均衡约束的非光滑半无限规划问题与其混合对偶问题之间的强弱对偶定理.The properties of nonsmooth semi-infinite programming problems with equilibrium constraints are discussed in this paper.By using convexificators,the mixed dual model for the nonsmooth sem-infinite programming problems with equilibrium constraints are proposed.Different from the convexity in traditional duality theory,∂*-convex and∂*-invex assumptions are considered by convexificators.In this paper,the weak duality theorem and strong duality theorem are established between nonsmooth semi-infinite programming with equilibrium constraints and its dual problem.

关 键 词：半无限规划 均衡约束 凸化集 对偶 

分 类 号：O224[理学—运筹学与控制论]