(h,φ)-凸函数的广义方向导数及其性质  

Generalized Directional Derivative of (h;φ)-Convex Function and its Properties

作　　者：徐义红[1] 

机构地区：[1]南昌大学基础部,江西南昌330029

出　　处：《南昌大学学报（工科版）》2002年第4期81-84,共4页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金(69972036);江西省自然科学基金资助

摘　　要：方向导数在非线性规划中对启发和研究某些最优性准则及计算方法是特别有用的.本文借助于Ben-Tal广义代数运算针对(h,φ)-凸函数定义了一种广义方向导数,它是凸函数方向导数的推广.给出了用凸函数方向导数计算广义方向导数的公式.引进了(h,φ)-可微函数的概念.得到了一类(h,φ)-凸且(h,φ)-可微函数的广义方向导数与(h,φ)-微分之间的关系式.最后用广义方向导数刻画了广义次梯度.The concept of directional derivatives is particularly useful in the motivation and development of some optimality criteria and computational procedures in nonlinear programming.With the help of Ben-Tal generalized algebraic operations,a kind of generalized directional derivatves for (h,φ)-convex functions is defined,which is a generalization of directional derivatives for convex functions.The formula is given for calculating generalized directional derivative by using the directional derivative of convex functions.The concept of (h,φ)-differentiable functions is introduced.The relationship between (h,φ)-differential and generalized directional derivative is presented for a class of (h,φ)-convex and (h,φ)-differentiable functions.Finally,The subdifferential is characterized by utilizing the generalized directional derivative.

关 键 词：性质 (h φ)-凸函数 广义方向导数 广义次梯度 广义次微分 最优化 

分 类 号：O224[理学—运筹学与控制论]