凸锥的一个广义内部性质

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

凸锥的一个广义内部性质赵克全, 夏远梅重庆师范大学数学科学学院, 重庆 401331 A Characterization of Convex Cone Via Generalized Interior ZHAO Kequan, XIA YuanmeiCollege of Mathematics Science, Chongqing Normal University, Chongqing 401331

摘要
图/表
参考文献(0)
相关文章(3)
点击分布统计
下载分布统计
-->

全文: PDF(283 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要在集合的拟内部和相对代数内部非空的条件下给出了凸锥的一个广义内部性质,证明了凸锥的拟内部和相对代数内部的一致性,进而建立了基于凸锥的拟内部和相对代数内部的非凸分离定理.此外,也给出了一些具体例子对主要结果进行了解释.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2015-03-05

PACS:

O221.6

基金资助:国家自然科学基金重点项目(11431004),国家自然科学基金项目(11301574,11271391),重庆市基础与前沿研究计划项目(cstc2015jcyjA00027),重庆市教委科学技术研究项目(KJ1500303),第二批重庆市高等学校青年骨干教师资助计划项目,重庆市研究生科研创新项目(CYS15154)资助.

引用本文:

赵克全, 夏远梅. 凸锥的一个广义内部性质[J]. 应用数学学报, 2016, 39(2): 289-297. ZHAO Kequan, XIA Yuanmei. A Characterization of Convex Cone Via Generalized Interior. Acta Mathematicae Applicatae Sinica, 2016, 39(2): 289-297.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2016/V39/I2/289

[1]	Chen G Y, Huang X X, Yang X Q. Vector Optimization:Set-valued and Variational Analysis. Berlin:Springer-Verlag, 2005
[2]	Yang X M, Yang X Q, Chen G Y. Theorems of the alternative and optimization with set-valued maps. Journal of Optimization Theory and Applications, 2000, 107(3):627-640
[3]	Yang X M, Li D, Wang S Y. Near-subconvexlikeness in vector optimization with set-valued functions. Journal of Optimization Theory and Applications, 2001, 110(2):413-427
[4]	Rong W D, Wu Y N. Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps. Mathematical Methods of Operations Research, 1998, 48(2):247-258
[5]	高英. 多目标优化ε-拟弱有效解的最优性条件. 应用数学学报, 2010, 33(6):1061-1071 REF (Gao Y. Optimality conditions for ε-quasi weakly efficient solution in multiobjective optimization problems. Acta Mathematicae Applicatae Sinica, 2010, 33(6):1061-1071)
[6]	Rockafellar R T. Convex Analysis. New Jersey:Princeton University Press, 1970
[7]	Limber M A, Goodrich R K. Quasi interiors, lagrange multipliers, and ssize Lp spectral estimation with lattice bounds. Journal of Optimization Theory and Applications, 1993, 78(1):143-161
[8]	Borwein J M, Lewis A S. Partially finite convex programming, Part I quasi relative interiors and duality theory. Mathematical Programming, 1992, 57(1-3):15-48
[9]	Borwein J, Goebel R. Notions of relative interior in Banach spaces. Journal of Mathematical Sciences, 2003, 115(4):2542-2553
[10]	史树中. 凸分析. 上海:上海科学技术出版社, 1990 REF (Shi S Z. Convex Analysis. Shanghai:Shanghai Science and Technology Press, 1990)
[11]	Boc? R I, Csetnek E R. Regularity conditions via generalized interiority notions in convex optimization:new achievements and their relation to some classical statements. Optimization, 2012, 61(1):35-65
[12]	Adán M, Novo V. Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness. European Journal of Operational Research, 2003, 149(3):641-653
[13]	Adán M, Novo V. Proper efficiency in vector optimization on real linear spaces. Journal of Optimization Theory and Applications, 2004, 121(3):515-540
[14]	Bao T Q, Mordukhovich B S. Relative Pareto minimizers for multiobjective problems:existence and optimality conditions. Mathematical Programming, 2010, 122(2):301-347
[15]	Zhou Z A, Yang X M. Optimality conditions of generalized subconvexlike set-valued optimization problems based on the quasi-relative interior. Journal of Optimization Theory and Applications, 2011, 150(2):327-340
[16]	Göpfert A, Tammer C, Riahi H, et al. Variational Methods in Partially Ordered Spaces. New York:Springer-Verlag, 2003
[17]	Flores-Bazán F, Hernández E. A unified vector optimization problem:complete scalarizations and applications. Optimization, 2011, 60(12):1399-1419
[18]	Tammer C, Zu?linescu C. Lipschitz properties of the scalarization function and applications. Optimization, 2010, 59(2):305-319
[19]	Zhao K Q, Xia Y M, Yang X M. Nonlinear scalarization characterizations of E-efficiency in vector optimization. Taiwanese Journal of Mathematics, 2015, 19(2):455-466

[1]	阎爱玲, 修乃华. 欧几里德若当代数向量优化问题的谱标量化[J]. 应用数学学报(英文版), 2008, 31(5): 940-952.
[2]	李永祥. 四阶边值问题正解的存在性与多解性[J]. 应用数学学报(英文版), 2003, 26(1): 109-116.
[3]	李仲飞. 集值映射向量优化的Benson真有效性[J]. 应用数学学报(英文版), 1998, 21(1): 0-0.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14151