广义Minty 向量似变分不等式解的性质

数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1732-1742.

广义Minty 向量似变分不等式解的性质

韩山师范学院数学与信息技术系广东潮州 521041

收稿日期:2007-10-08 修回日期:2008-09-16 出版日期:2009-12-25 发布日期:2009-12-25
基金资助:
国家自然科学基金(60574075)资助

Properties of the Solution in Generalized Minty Vector Variational-like Inequalities

Department of Mathematics and Information Technology, Hanshan Normal University, Guangdong Chaozhou 521041

Received:2007-10-08 Revised:2008-09-16 Online:2009-12-25 Published:2009-12-25
Supported by:
国家自然科学基金(60574075)资助

摘要/Abstract

摘要：

在拓扑向量空间中讨论下Dini方向导数形式的广义Minty向量似变分不等式问题. 可微形式的Minty变分不等式、Minty似变分不等式和Minty向量变分不等式是其特殊形式. 该文分别讨论了Minty向量似变分不等式的解与径向递减函数, 与向量优化问题的最优解或有效解之间的关系问题, 以及Minty向量似变分不等式的解集的仿射性质. 这些定理推广了文献中Minty变分不等式的一些重要的已知结果.

关键词: 向量似变分不等式, 不变凸集, 不变凸函数, 径向递减函数

Abstract:

Generalized Minty vector variational-like inequalities as being of lower Dini directional derivative type are studied in topological vector spaces, which include Minty variational inequalities, Minty variational-like inequalities and Minty vector variational inequalities as being of differential type. Some relations between solutions of Minty vector
variational-like inequalities and solutions of vector optimization problems, as well as radial decrease properties of functions, are investigated. Moreover, the affine solution sets of Minty vector variational-like inequalities are
presented. As consequences, some recent known results in literature are obtained in the special case.

Key words: Vector variational-like inequality, Invex set, Invex function, Radial decrease function

中图分类号:

49J20

肖刚, 刘三阳. 广义Minty 向量似变分不等式解的性质[J]. 数学物理学报, 2009, 29(6): 1732-1742.

XIAO Gang, LIU San-Yang. Properties of the Solution in Generalized Minty Vector Variational-like Inequalities[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1732-1742.

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