非线性凸半定规划的最优性条件

Optimality Conditions in Nonlinear Convex Semidifinite Programming

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.