非可微r-不变凸函数的η-鞍点条件  

η -saddle Point Condition for Non-differentiable r -invexity Functions

作　　者：袁静 李向有[1] 刘文艳 YUAN Jing;LI Xiangyou;LIU Wenyan(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《贵州大学学报（自然科学版）》2023年第6期18-23,共6页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(11961072);陕西省教育厅科研资助项目(17JK0860);延安大学校级科研计划资助项目(YDY2020-24)。

摘　　要：利用η-逼近法,定义了η-鞍点和η-Lagrange函数。研究了一类包含r-不变凸函数的非线性数学规划问题的鞍点条件,得到了η-近似优化问题下的η-鞍点最优性准则和原规划的最优解与η-近似优化问题下的η-Lagrange鞍点的等价性,用新的方法推广了相关鞍点结论。This paper uses theη-approximation method to define theη-saddle point andη-Lagrange functions.The saddle point conditions of a class of nonlinear mathematical programming problems including r-invex functions are studied,and theη-saddle point optimality criterion under theη-approximation optimization problem and the optimal solution of the original program and the equivalence of theη-Lagrange saddle point under theη-approximation optimization problem are obtained,and the relevant saddle point conclusion is generalized by the new method.

关 键 词：η逼近方法 η-鞍点 r-不变凸函数 η-Lagrange函数 

分 类 号：O221.6[理学—运筹学与控制论] O224[理学—数学]