非光滑多目标区间优化的最优性条件  

Optimality conditions on nonsmooth vector interval-valued optimization

作　　者：钱鑫强 王开荣[1] QIAN Xin-qiang;WANG Kai-rong(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《山东大学学报（理学版）》2020年第11期26-34,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11571055)。

摘　　要：利用Clarke方向导数和Clarke次微分得到了非光滑多目标区间优化弱LU有效解的Fritz John最优必要条件。在广义不变凸性及函数正则性的假设下得到了KKT条件、充分性条件及相关对偶理论。利用了一些实例来验证理论的可行性,这些结论能够解决一般情形下多目标区间优化的相关问题。By using Clarke directional derivative and Clarke subdifferential,Fritz John optimal necessary conditions for weak LU efficient solutions of nonsmooth vector interval-valued optimization are obtained.Under the assumption of generalized invariant convexity and regularity of functions,KKT necessary optimality conditions,sufficient optimality conditions and related duality results are given.Some examples are used to verify the feasibility of the theory.These conclusions can solve the related problems of vector interval-valued optimization in general.

关 键 词：区间优化 正则性 LU有效解 MOND-WEIR对偶 

分 类 号：O221[理学—运筹学与控制论]