DICR函数的刻画及其在优化问题中的应用

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 165-171.

DICR函数的刻画及其在优化问题中的应用

马世贵,李军*()

西华师范大学数学与信息学院四川南充 637009

收稿日期:2017-09-20 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 李军 E-mail:junli@cwnu.edu.cn; junli1026@163.com
基金资助:
国家自然科学基金(11371015);国家自然科学基金(11871059);四川省高校科研创新团队(16TD0019);西华师范大学英才科研基金(17YC379)

Characterizations of DICR Functions and Applications to Optimization Problems

Shigui Ma,Jun Li*()

Department of Mathematics and Information, China West Normal University, Sichuan Nanchong 637009

Received:2017-09-20 Online:2019-02-26 Published:2019-03-12
Contact: Jun Li E-mail:junli@cwnu.edu.cn; junli1026@163.com
Supported by:
the NSFC(11371015);the NSFC(11871059);the Innovation Team of Department of Education of Sichuan Province(16TD0019);the Meritocracy Research Funds of China West Normal University(17YC379)

摘要/Abstract

摘要：

在拓扑向量空间中研究DICR函数.引入该函数关于支撑集、次微分的概念，研究该函数支撑集、次微分之间的关系.也研究了与严格DICR函数相关的集合的最大元，得到严格DICR函数差的全局最小值的充要条件.

关键词: DICR函数, 支撑集, 次微分, 最大元, 全局最小值

Abstract:

In this paper, we study DICR functions in topological vector spaces. We introduce support sets and subdifferential of DICR functions, discuss the relations between support sets and subdifferential. We also investigate maximal elements of the set involving strictly DICR functions and present necessary and sufficient conditions for the global minimum of the difference of two strictly DICR functions.

Key words: DICR functions, Support set, Subdifferential, Maximal elements, Global minimum

中图分类号:

O221

马世贵,李军. DICR函数的刻画及其在优化问题中的应用[J]. 数学物理学报, 2019, 39(1): 165-171.

Shigui Ma,Jun Li. Characterizations of DICR Functions and Applications to Optimization Problems[J]. Acta mathematica scientia,Series A, 2019, 39(1): 165-171.

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