一类新的非凸鲁棒优化问题的混合型对偶  

Mixed Type Duality for a New Class of Non-Convex Robust Optimization Problems

作　　者：王梦丹 王娇浪 WANG Mengdan;WANG Jiaolang(College of Science,Hunan University of Science and Engineering,Yongzhou 425199,Hunan China;College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

机构地区：[1]湖南科技学院理学院,湖南永州425199 [2]吉首大学数学与统计学院,湖南吉首416000

出　　处：《吉首大学学报（自然科学版）》2024年第1期7-12,共6页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(12261037);湖南省教育厅科学研究项目(21C0699);湖南科技学院科学研究项目(21XKY037)。

摘　　要：引入了一类目标函数和约束函数均为α-凸函数的新的非凸鲁棒优化问题,并定义了其混合型对偶问题.利用Frechet次微分的性质构建了近似解的最优性条件,并建立了原问题与混合型对偶问题之间的弱对偶、强对偶和逆对偶理论.We first introduced a new class of non-convex robust optimization problems,whose objective functions and constraint functions areα-convex functions and defined the mixed-type approximate dual problem of the new problems.Then,by using the properties of the Frechet subdifferentials,the optimality conditions of approximate solution are introduced.At the same time,some results for the weak duality,strong duality and converse-like duality theorems between the non-convex robust optimization problem and its mixed type dual problem are also given.

关 键 词：鲁棒优化 Frechet次微分 混合型对偶 

分 类 号：O221.2[理学—运筹学与控制论]