The maximal value point s problem of a convex function on a closed convex subset in locally convex space is considered by using the level set of function,-subdifferential and-normal cone . it gives several equivalent characters on the optimal solutions of the problem 利用函数的水平集,-次微分和-法向锥等工具研究局部凸空间的凸函数在闭凸子集上的最大值点问题,给出了最优解的几个等价刻划
Let f ( x ) and f ( x ) stand for the generalized gradients proposed by clarke and xu yihong respectively . three of generalized gradients are compared and the inclusion relation between them is so the set of the generalized gradient defined in this paper is smaller; they coincide when / is a convex function or f is differentiable 文中对三类广义梯度进行比较,若以和分别表示clarke和徐义红定义的广义梯度,三者之间的包含关系为即本文定义的广义梯度集合较小;而当f为凸函数或f可微时,三者统一。
General convex sets and convex functions : g-convex sets and g-convcx functions are investigated, some properties of which arc achieved, the cti-tcrions of g-convcx functions and g-quasiconvcx functions arc given, the theory of general convexity is deepen : two kinds of general variational inequality problems are studied 讨论了一类广义的凸集和凸函数:g-凸集和g-凸函数,得出了若干性质,给出了g-凸函数和g-拟凸函数的判别准则,丰富了广义凸性的内容;研究了两类广义的变分不等式问题。