具有范数结构凸多目标优化问题的最优性条件  

Optimality Conditions for Convex Multi-Objective Optimization Problems with Norm Structure

作　　者：陈洁 夏远梅 赵克全 CHEN Jie;XIA Yuanmei;ZHAO Kequan(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2024年第3期1-8,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金——重大项目(No.11991024),面上项目(No.12171063,No.12101096);重庆市高校创新研究群体项目(No.CXQT20014);重庆市自然科学基金面上项目(No.cstc2022ycjh-bgzxm0114,No.cstc2021jcyj-msxmX0280);重庆市教育委员会科学技术研究项目(No.KJQN202100521)。

摘　　要：研究一类具有范数结构特殊多目标优化问题的最优性条件。通过计算该类问题目标函数的广义次微分,系统论述了Pareto有效解的FJ最优性条件和KKT最优性条件,并基于这些定理定义了新的Pareto-FJ稳定点和Pareto-KKT稳定点,提出并证明了这2类稳定点的等价条件,以及它们对应的几何最优性条件。针对带有一般约束和区间约束的一类具范数结构凸多目标优化问题,建立了Pareto-FJ最优性条件、Pareto-KKT最优性条件等一系列定理。所得结果丰富了多目标优化理论,为具有范数结构多目标优化问题的应用研究打下基础。The aim is to investigate the optimality conditions for a specific class of multi-objective optimization problems with a norm structure.The Fritz-John and Kuhn-Tucker necessary optimality conditions for the Pareto optimum are systematically examined by calculating the subdifferential of the objective functions of these problems.Theorems are utilized to establish the definitions of novel Pareto-FJ and Pareto-KKT stationary points.Additionally,equivalence conditions for these stationary points,together with their related geometric optimality conditions,are presented and then proven.Several theorems such as the Pareto-FJ optimality condition and the Pareto-KKT optimality condition are established for a class of norm-structured convex multi-objective optimization problems with general constraints and interval constraints.The results obtained enrich the theory of multi-objective optimization and provide a foundational basis for the applied research of multi-objective optimization problems with a normative structure.

关 键 词：多目标优化问题 范数结构 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]