广义向量变分不等式和广义对偶模型

李月鲜;戎卫东;刘海军

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 786-799.

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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 786-799. DOI: 10.12341/jssms08418
论文

广义向量变分不等式和广义对偶模型

    李月鲜(1), 戎卫东(2), 刘海军(3)
作者信息 +

The Generalized Vector Variational Inequalities and the Generalized Dual Models

    LI Yuexian(1), RONG Weidong(2), LIU Haijun(3)
Author information +
文章历史 +

摘要

研究实Banach空间中带有不等式约束的非光滑向量优化问题(VP).首先,借助下方向导数引进了
广义Minty型向量变分不等式，并通过变分不等式来探讨问题(VP)的最优性条件.接着,利用函数的上次微分构造了不可微向量优化问题(VP)的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理.

Abstract

In this paper, the nonsmooth vector optimization problem with inequality constraints in real Banach space is studied. First, in terms of the lower directional derivatives, the generalized Minty type vector variational inequalities are introduced. Then, the optimality condition of the problem (VP) is obtained.
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.

关键词

下方向导数 / 广义Minty型向量变分不等式 / 广义对偶模型.

Key words

Lower directional derivative / generalized Minty type vector variational inequality / generalized dual model.

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李月鲜 , 戎卫东 , 刘海军. 广义向量变分不等式和广义对偶模型. 系统科学与数学, 2009, 29(6): 786-799. https://doi.org/10.12341/jssms08418
LI Yuexian , RONG Weidong , LIU Haijun. The Generalized Vector Variational Inequalities and the Generalized Dual Models. Journal of Systems Science and Mathematical Sciences, 2009, 29(6): 786-799 https://doi.org/10.12341/jssms08418
中图分类号： 49N45   
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