非线性凸半定规划的最优性条件  

Optimality Conditions in Nonlinear Convex Semidifinite Programming

作　　者：陈秀宏[1] 

机构地区：[1]淮阴师范学院数学系,江苏淮安223300

出　　处：《淮阴师范学院学报（自然科学版）》2006年第2期94-98,共5页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：江苏省教育厅自然科学基金资助项目(03KJB110012)

摘　　要：考虑非线性凸半定规划问题,引入了矩阵函数广义梯度和广义方向导数的定义,讨论了凸矩阵函数的一些性质.并给出了非线性半定规划的最优性必要和充分条件.The optimality conditions in nonlinear convex semidefinite programming are considered. First, the definitions of generalized gradient and generalized directional derivative for nonlinear matrix function are introduced. Some properties are obtained when the matrix function is convex. Finally, optimality necessary and sufficient conditions for nonlinear convex semidefinite programming are proved.

关 键 词：非线性半定规划 凸矩阵函数 广义梯度 广义方向导数 最优性条件 

分 类 号：O221.2[理学—运筹学与控制论]