非光滑半无限多目标优化的高阶KKT最优性充分条件  

Higher-Order KKT Sufficient Optimality Conditions for Nonsmooth Semi-Infinite Multiobjective Optimization

作　　者：曹琪 冯敏 CAO Qi;FENG Min(School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,P.R.China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《应用数学和力学》2024年第4期502-508,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12201085);重庆市自然科学基金(CSTB2023NSCQ-MSX0332)。

摘　　要：考虑了一类非光滑半无限多目标优化问题.利用高阶Studniarski下导数,得到了问题的严格局部有效解的高阶弱KKT最优性充分条件.进一步地,若假设该最优性条件中目标函数相关的乘子均大于零,则得到严格局部Borwein真有效解的高阶强KKT充分条件.这些充分条件适用于处理无任何凸性假设下的问题.The nonsmooth semi-infinite multiobjective optimization problems were investigated.The higher-order weak KKT sufficient optimality conditions for strictly local efficient solutions were established in terms of higher-order lower Studniarski derivatives.Furthermore,under the assumption that all multipliers associated with objective functions are positive in optimality conditions,the higher-order strong KKT sufficient optimality conditions for strictly local Borwein-properly efficient solutions would be achieved.These sufficient optimality conditions were established without any convexity assumptions.

关 键 词：半无限多目标优化 高阶Studniarski下导数 高阶KKT充分条件 

分 类 号：O221.6[理学—运筹学与控制论]