二次约束凸规划的边际函数的一阶ε—方向导数

FIRST ORDER ε-DIRECTIONAL DERIVATIVE OF MARGINAL FUNCTION OF A QUADRIC CONVEX PROGRAMMING

文[1]讨论了线性约束凸规划的边际函数的ε—可微性,本文在此基础上讨论了二次凸规划Min{f(y)丨y^TAy≤x,y∈R^n,x∈R}问题,证明了二次凸规划的边际函数φ(x)是ε—可微的,并把求φ(x)的一阶ε—方向导数的问题表示成求解一非线性规划的最优值,从而可利用非线性规划方法来确定φ(x)的一阶ε—方向导数。

In paper(1) , the ε-directional derivatives of a marginal function in convex programming with linear constraints had been discussed. Based on that, We have proved the ε-differentiability of ths marginal function of a quadric convex programming in this paper, and further expressed the first order ε-directional derivative as the optimal value of a nonlinear programming.