鲁棒凸优化问题拟近似解的刻划  

Characterizations of Quasi Approximate Solution for RobustConvex Optimization Problems

作　　者：孔翔宇 刘三阳 KONG Xiangyu;LIU Sanyang(School of Mathematics and Information Science,Xianyang Normal University,Xianyang 712000,China;School of mathematics and statistics,Xidian University,xi'an 710071,China)

机构地区：[1]咸阳师范学院数学与信息科学学院,陕西咸阳712000 [2]西安电子科技大学数学与统计学院,陕西西安710071

出　　处：《应用数学》2020年第3期634-642,共9页Mathematica Applicata

基　　金：宁夏高等学校科学研究项目(NGY2017158)。

摘　　要：本文研究鲁棒凸优化问题拟近似解的最优性条件和对偶理论.首先利用鲁棒优化方法,在由约束函数的共轭函数的上图给出的闭凸锥约束规格条件下,建立了拟近似解的最优性充要条件.其次给出了鲁棒凸优化问题拟近似解在Wolf型和Mond-weir型对偶模型下的强(弱)对偶定理.最后给出具体实例验证了本文获得的结果.In this paper,we study quasi approximate solution for a robust convex optimization problem in the face of data uncertainty.By using the robust optimization approach,we first establish optimality conditions for quasi approximate solution under a closed convex cone constraint qualification which is given by conjugate function for the constraint function.In addition,we also characterizeWolf type and Mond-weir type duality theorems for quasi approximate solution on the robust convex optimization problem.Moreover,some examples are given to illustrate the obtained results.

关 键 词：鲁棒凸优化 次微分 拟近似解 最优性条件 对偶理论 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]