非光滑半无限优化的最优性必要条件  

Necessary Conditions of Nonsmooth Semi-Infinite Programming

作　　者：徐茂杨 高英 XU Maoyang;GAO Ying(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）》2022年第2期8-14,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11771064);重庆市科学技术研究重点项目(No.KJZDK202001104);重庆市高校创新研究群体项目(No.CXQT20014);重庆市留学人员回国创业创新支持计划(No.cx2020096)。

摘　　要：【目的】研究非光滑半无限优化问题在极限次微分下的最优性必要条件。【方法】通过约束品性和择一定理,研究带有抽象集约束的非光滑半无限优化问题的Kuhn-Tucker型必要条件。【结果】首先,举例说明已有文献中关于非光滑半无限优化问题的必要性条件的错误,并给出合理的修正。随后,针对半无限优化问题,给出一类约束品性。并通过择一定理得到了带有抽象集约束的非光滑半无限优化问题的Kuhn-Tucker型必要条件。【结论】所得结果丰富了半无限优化理论。[Purposes]To study the necessary optimality conditions of nonsmooth semi-infinite optimization problem under limiting subdifferential. [Methods] The Kuhn-Tucker-type necessary condition for nonsmooth semi-infinite optimization problems with abstract set constraint is studied by using constraint qualification condition and alternative theorem. [Findings] First, examples are given to illustrate the errors in the necessary conditions of nonsmooth semi-infinite optimization problem in the existing literature, and reasonable corrections are given. Then, aiming at the semi-infinite optimization problem, a class of constraint qualification condition is given. The Kuhn-Tucker type necessary condition for nonsmooth semi-infinite optimization problems with abstract set constraint is obtained by using an alternative theorem. [Conclusions]The results obtained are of great significance to the semi-infinite optimization theory.

关 键 词：半无限优化 极限次微分 约束品性 最优性必要条件 

分 类 号：O221.2[理学—运筹学与控制论]