English

运筹学学报 >

2016 , Vol. 20 >Issue 1: 54 - 60

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.01.005

运筹学

向量优化问题中的弱S-有效解

展开
  • 1. 重庆师范大学数学科学学院, 重庆 401331; 2. 上海大学理学院, 上海 200444

收稿日期: 2015-03-20

  网络出版日期: 2016-03-15

基金资助

国家自然科学基金重点项目(No. 11431004), 国家自然科学基金(Nos. 11301574,11271391), 重庆市教委科学技术研究项目(No. KJ1500310)

收起

Weak S-efficient solution of vector optimization

Expand
  • 1. College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China; 2. College of Science, Shanghai University, Shanghai 200444, China

Received date: 2015-03-20

  Online published: 2016-03-15

Fold

摘要

在局部凸拓扑线性空间中, 提出了集值向量优化问题的弱S-有效解和S-次似凸性概念. 在S-次似凸性假设下建立了择一性定理, 并利用择一性定理建立了弱S-有效解的标量化定理. 此外, 通过几个具体例子解释了主要结果.

关键词： 向量优化; S-次似凸; 弱S-有效解; 择一性定理; 标量化定理

本文引用格式

郭辉, 白延琴 . 向量优化问题中的弱S-有效解[J]. 运筹学学报, 2016 , 20(1) : 54 -60 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.005

Abstract

In this paper, we introduce the concept of weak S-optimal solution and S-subconvexlikeness of vector optimization with set-valued maps and obtain an alternative theorem in a real locally Hausdorff topological vector space. Furthermore, under the assumption of S-subconvexlikeness, we establish scalarization theorem for weak S-efficient solution. We also give some examples to illustrate the main results.

Key words： vector optimization; S-subconvexlikeness; weak S-efficient solution; alternative theorem; scalarization theorem

参考文献

[1] Jahn J. Vector Optimization: Theory, Applications, and Extensions[M]. Berlin: Springer, 2004.
[2] Ehrgott M.  Multicriteria Optimization [M]. Berlin: Springer, 2005.
[3] Chen G Y, Huang X X, Yang X Q. Vector Optimization: Set-Valued and Variational Analysis [M]. Berlin: Springer, 2006.
[4] Yang X M, Li D, Wang S Y. Near-subconvexlikeness in vector optimization with set-valued functions [J]. Journal of Optimization Theory and Applications, 2001, 110: 413-427.
[5] Zhao K Q, Yang X M. Characterizations of efficient and weakly efficient points in nonconvex vector optimization [J]. Journal of Global Optimization, 2014, Doi: 10.1007/s10898-014-0191-1.
[6] Rong W D, Wu Y N. \varepsilon-weak minimal solutions of vector optimization problems with set-valued maps [J]. Journal of Optimization Theory and Applications, 2000, 106: 569-579.
[7] Gutierrez C, Jimenez B, Novo V. A unified approach and optimality conditions for approximate solutions of vector optimization problems [J]. SIAM Journal on Optimization, 2006, 17: 688-710.
[8] Chicco M, Mignanego F, Pusillo L, et al. Vector optimization problems via improvement sets [J]. Journal of Optimization Theory and Applications,  2011, 150: 516-529.
[9] Gutierrez C, Jimenez B, Novo V. Improvement sets and vector optimization [J]. European Journal of Operational Research, 2012, 223: 304-311.
[10] Zhao K Q, Yang X M, Peng J W. Weak E-optimal solution in vector optimization [J]. Taiwanese Journal of Mathematics, 2013, 17: 1287-1302.
[11] Zhao K Q, Yang X M. E-Benson proper efficiency in vector optimization [J]. Optimization, 2013, Doi: 10.1080/02331934.2013.798321.
[12] Zhao K Q, Chen G Y, Yang X M. Approximate proper efficiency in vector optimization [J]. Optimization, 2014, Doi: 10.1080/02331934.2014. 979818.
[13] Zhao K Q, Yang X M. A unified stability result with perturbation in vector optimization [J]. Optimization Letters, 2013, 7: 1913-1919.
[14] Flores-Bazan F, Hernandez E. A unified vector optimization problem: complete scalarizations and applications [J]. Optimization, 2011, 60: 1399-1419.
[15] Gutierrez C, Jimenez B, Novo, V. On approximate efficiency in multiobjective programming [J]. Mathematical Methods of Operational Research, 2006, 64: 165-185.
[16] Li Z M. A theorem of the alternative and its application to the optimization of set-valued maps [J]. Journal of Optimization Theory and Applications, 1999, 100: 365-375.
[17] Li Z F, Chen G Y. Lagrangian multipliers, saddle points, and duality in vector optimization of set-valued maps [J]. Journal of Mathematical Analysis and Applications, 1997, 215: 297-316.
Options
文章导航

/

〈 〉