1) subconvex function
次凸泛函
1.
In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.
在巴拿赫空间理论中,Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一,分隔性定理是Hahn-Banach定理的重要应用,本文利用"超平面"的方法,改进了一个分隔性定理的证明;另外,本文利用邻域的"平移"方法,给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。
2) explicit convex
显凸泛函
1.
In this paper,the concept of explicit convex function is given,then tow sufficient conditions of explicit convex functions are obtained by using G-differentiability of functions in Banach space.
在Banach空间中给出了显凸泛函的概念,然后利用泛函的G-可微性,给出了显凸泛函的两个充分条件。
3) convex functional
凸泛函
1.
Based on Hahn Banach functional extension theorem,the extension of linear functional is proved for wider functional type——convex functional type,and the result of theorem 2 is obtained.
:在哈恩 -巴拿赫泛函延拓定理的基础上 ,对更广泛的泛函类——凸泛函类 ,证明了线性泛函的可延拓性 。
2.
In this paper, we defined a new kind of generalized F convex functions by introducing a convex functional F several sufficient conditions for nonsmooth optimization problems have been presented.
通过引入凸泛函F定义了一类新的广义凸函数 ,并在此凸性下讨论了非光滑最优化问题的充分性条件 。
3.
in this paper, a class of inequalities of convex functional are given, as their applications.
给出了凸泛函的一类不等式，作为其应用，推广了一些已有文献中的主要结果。
4) A Family of Convex Functional
凸泛函族
5) α-convex functional
α-凸泛函
6) strongly convex functions
强凸泛函
补充资料：凸凸
1.高出貌。
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