二次约束凸规划的边际函数的一阶ε—方向导数

doi:10.3863/j.issn.1000-2634.1992.02.15

西南石油大学学报(自然科学版) ›› 1992, Vol. 14 ›› Issue (2): 111-116.DOI: 10.3863/j.issn.1000-2634.1992.02.15

二次约束凸规划的边际函数的一阶ε—方向导数

张明泉

(管理工程系)

收稿日期:1991-04-12 修回日期:1900-01-01 出版日期:1992-04-20 发布日期:1992-04-20

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

Zhang Ming-quan

(Department of Mlanagement Engineering)

Received:1991-04-12 Revised:1900-01-01 Online:1992-04-20 Published:1992-04-20

摘要/Abstract

摘要： 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)」yTAy≤x，y∈Rn，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。

关键词: 方向导数, 边际导数, 凸规划, 非线性规划

Abstract: 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。一differentiability of the 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.

Key words: Directional derivative, Marginal function, Convex programming, Nonlinear programming

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