期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

非线性标量化函数与向量优化问题的适定性

Nonlinear Scalarization Functions and Well Posedness in Vector Optimization
下载PDF
导出
摘要 定义一类非线性标量化函数,给出具有可变锥结构的向量优化问题的DH-适定和B-适定的概念。利用这类非线性标量化函数,把具有可变锥结构的向量优化问题转化为数值优化问题,然后研究这类数值优化问题与原可变锥结构的向量优化问题适定性之间的关系。 A class of nonlinear scalarization functions is defined.DH-well posedness and B-well posedness of vector optimization problems with variable cone structure are given.By applying this nonlinear scalarization function,a vector optimization problem under variable cone structure is convert to a scalar optimization problem.Moreover,the relationships of well posedness between this class of scalar optimization problems and vector optimization problems with variable cone structure are studied.
作者 肖刚
机构地区 韩山师范学院数学与信息技术系
出处 《南昌大学学报（理科版）》 CAS 北大核心 2010年第4期341-345,共5页 Journal of Nanchang University(Natural Science)
基金 国家自然科学基金资助项目(60703118)
关键词 向量优化问题 非线性标量化函数 适定性 极小序列 vector optimization problem nonlinear scalarization function well posedness minimizing sequence
分类号 O178 [理学—基础数学]
  • 相关文献

参考文献10

  • 1DONTCHEV A L,ZOLEZZI T. Well- Posed Optimization Problems, Lecture Notes in Mathematics [ M ]. Berlin Springer Verlag, 1993,1543.
  • 2PUSILLO L. Well Posedness and Optimization Problems, Variational Analysis and Applications [ J ]. Springer, 2005 : 889 - 904.
  • 3徐义红,肖明丽.集值映射的超有效广义梯度[J].南昌大学学报（工科版）,2008,30(2):127-130. 被引量：6
  • 4GoPFERT A, RIHAI H, TAMMER C, et al.. Variational Methods in Partially - Ordered Spaces, CMS Books in Mathematics [ M ]. New York, Springer Verlag,2003,17.
  • 5MIGLIERINA E, MOLHO E, ROCCA M. Well - Posedness and Scalarization in Vector Optimization [ J ]. Journal of Optimization Theory and Applications, 2005,126 ( 2 ) : 391 - 409.
  • 6CHEN G Y, YANG X Q, Yu H. A Nonlinear Scalarization Function and Generalized Quasi - vector Equilibrium Problems [ J ]. Journal of Global Optimization, 2005,32 : 451 - 466.
  • 7CHEN G Y, YANG X Q. Characterizations of Variable Domination Structures Via a Nonlinear Scalarization [ J ]. Journal of Optimizaton Theory and Applications, 2002, 112: 97-110.
  • 8CHEN G Y, GOH C J, YANG X Q. Vector Network Equilibrium Problems and Nonlinear Scalarization Methods [ J ]. Mathematical Methods of Operations Research, 1999,49:239 - 253.
  • 9LIN L J, ANSARI Q H, HUANG Y J. Some Existence Results for Solutions of Generalized Vector Quasi - equilibrium Problems [ J ]. Math Meth Oper Res, 2005,65 : 85 - 98.
  • 10CRESPI G P, GINCHEV I, ROCCA M. Variational Inequalities in Vector Optimization, Variational Analysis and Applications [ M ]. Dordrecht Kluwer Academic, 2004 : 259 - 278.

二级参考文献9

  • 1徐义红,刘三阳.SUPER EFFICIENCY IN THE NEARLY CONE-SUBCONVEXLIKE VECTOR OPTIMIZATION WITH SET-VALUED FUNCTIONS[J].Acta Mathematica Scientia,2005,25(1):152-160. 被引量：14
  • 2徐义红.集值优化问题的最优条件[D].西安:西安电子科技大学博士学位论文,2004.
  • 3Khan J. Generalized Contingent Epiderivatives in Set-valued Optimization : Optimality Conditions [ J ]. Numerical Functional Analysis and Optimization, 2002,23 ( 5 ) : 807 -831.
  • 4Hu Y D, Ling C. Connectedness of Cone Superefficient Point Sets in Locally Convex Toplolgical Vector Spaces [J]. J Optim Theory Appl,2000,107(2) :433 -446.
  • 5Zheng X Y. Proper Efficiency in Locally Convex Toplolgical Vector Spaces [J]. J Optim Theory Appl, 1997,94 (2) :469 -486.
  • 6Li 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.
  • 7Luc D T. Contingent Derivatives of Set-valued Maps and Applications to Vector Optimization [ J ]. Mathematical programming, 1991,50:99 - 111.
  • 8Sawaragi Y, Tanino T. Conjugate Maps and Duality in Muhiobjective Optimization [ J ]. J Optim Theory Appl 1980 31:473 - 499.
  • 9Aubin J P, Frankowska H. Set-valued Analysis [ M ]. Basel : Birkhauser, 1990.

共引文献5

南昌大学学报（理科版）
2010年 第4期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部