集值映射多目标半定规划问题的epsilon-弱有效性

doi:10.15960/j.cnki.issn.1007-6093.2017.01.003

运筹学学报

集值映射多目标半定规划问题的epsilon-弱有效性

袁春红^1,*

1. 内蒙古师范大学数学科学学院, 呼和浩特 010022

收稿日期:2016-04-25 出版日期:2017-03-15 发布日期:2017-03-15
通讯作者: 袁春红 yuanchunhong1979@126.com
基金资助:
国家自然科学基金 (No. 11462020), 内蒙古教育厅项目 (No. NJZY032), 内蒙古师范大学科研基金项目 (No. 2014ZRYB09)

The epsilon-weak proper efficiency of multiobjective semidefinite programming with set-valued maps

YUAN Chunhong^1,*

1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China

Received:2016-04-25 Online:2017-03-15 Published:2017-03-15

摘要/Abstract

摘要：

对于集值映射多目标半定规划问题, 在近似锥-次类凸的框架下, 建立了含矩阵和向量的择一性定理, 给出了问题的epsilon-弱有效解的epsilon-Lagrange乘子定理及标量化定理和epsilon-弱鞍点定理．

关键词: 集值映射, 多目标半定规划, 近似锥-次类凸, epsilon-弱有效解, epsilon-Lagrange乘子, epsilon-弱鞍点

Abstract:

epsilon-weak efficient solutions of multiobjective semidefinite programming with set-valued maps are discussed. Under the condition of nearly
cone-subconvexlikeness, the alternative theorem which contained matrix and vector is established, then the epsilon-Lagrange multiplier theorem, the scalarization theorem and epsilon-weak saddle point theorem of the primal programming are obtained.

Key words: set-valued maps, multiobjective semidefinite programming, nearly cone-subconvexlikeness, epsilon-weak efficient solution, epsilon-Lagrange multiplier, epsilon-weak saddle point

袁春红. 集值映射多目标半定规划问题的epsilon-弱有效性[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2017.01.003.

YUAN Chunhong.

The epsilon-weak proper efficiency of multiobjective semidefinite programming with set-valued maps

[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.01.003.

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集值映射多目标半定规划问题的epsilon-弱有效性

The epsilon-weak proper efficiency of multiobjective semidefinite programming with set-valued maps

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