集值函数的广义共轭函数和次微分

Generalized Conjugate Functions and Subdifferentials for Set-Valued Functions

该文通过推广实函数的凸共轭函数及其次微分的概念,建立了一类关于集值函数的广义共轭函数及其次微分理论——集值函数的(H,Ω)共轭函数及(H,Ω)次微分理论。这一理论可以用来建立非线性规划问题的一类对偶性原理。

By extending the concepts of the convex conjugate func-tion and subdifferential for real-valued functions to the case for set-valued functions or point-to-set maps,this paper develops a theorem ofthe generalized conjugate function and subdifferential--the (H,Ω)conjugate function and (H, Ω) subdifferential theory, by means ofwhich,a class of the duality principle for nonlinear programming withset-valued objective functions and set-valued constraint functions canbe established.