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有效点、弱有效点和真有效点的锥刻画 被引量：3

CONE CHARACTERIZATIONS ABOUT PARETO, WEAK AND PROPER EFFICIENT POINTS
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摘要 利用集合在某点的相依切锥、法向锥和可行方向锥等研究向量优化问题的有效点、 弱有效点和真有效点的特征,对局部有效点、局部弱有效点和局部真有效点与集合的各 锥之间的关系作了刻画. The cone characterizations about Pareto,weak and proper efficient points are presented with the help of contingent, normal and feasible directions cones of a set at a point. Several kinds of locally efficient points are characterized with different cones.
作者 黄龙光 刘三阳
机构地区 西安电子科技大学应用数学系
出处 《系统科学与数学》 CSCD 北大核心 2003年第4期452-460,共9页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(69972036)资助课题
关键词 有效点 弱有效点 真有效点 锥刻画 向量 多目标规划 Pareto efficient points, weak efficient points, proper efficient points, locally efficient points, contingent cone, normal cone, feasible cone.
分类号 O221.6 [理学—运筹学与控制论]
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参考文献7

  • 1Kaisa Miettinen, Marko M and Makela. On cone characterizations of weak, proper and pareto optimality in multiobjective optimization. Mathematical Methods of Operations Research, 2001,53: 233-245.
  • 2Borwein J M. Proper efficient points for maximization with respect to cones. SIAM Journal on Control and Optimization, 1997, 15: 57-63.
  • 3Dauer J P and Saleh O A.A characterization of proper minimal problems as a solution of sublinear optimization problems, J Math Anal Appl, 1993, 178: 227-246.
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  • 5Guerraggio A, Molho E and Zaffaroni A. On the notion of proper efficiently in vector optimization.Journal of Optimization Theory and Applications, 1994, 82: 1-21.
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同被引文献19

  • 1赵克全.r-预不变凸函数的一个充分条件[J].重庆师范大学学报（自然科学版）,2006,23(1):10-13. 被引量：12
  • 2Kaisa M,Marko M M.On cone characterizations of weak、proper and pareto optimality in multiobjective optimization[J].Mathematical Methods of Operations Research,2001,53(2):233-245.
  • 3Cheng Y H,Fu W T.Strong efficiency in a locally concex space[J].Math Meth Oper Res,1999,50:373-384.
  • 4Zheng X Y.Proper efficiency in locally convex topological vector spaces[J].Journal of Optimization Theory and Applications,1997,94:469-486.
  • 5Borwein J M.Proper efficient points for maximization with respect to cones[J].Journal on Control and Optimization,1977,15:57-63.
  • 6Borwein J M,Zhuang D M.Super efficiency in convex vector optimization[J].ZOR,1991,35(3):175-184.
  • 7赵春英,戎卫东.强(严)有效点集的标量化[C].袁亚湘.中国运筹学会第八届学术交流会论文集.Hong Kong:Globallink Informatics Limited,2006,220-225.
  • 8KAISA M, MARKO M M. On cone characterizations of weak, proper and pareto optimality in multiobjective optimization [ J ]. Mathematical Methods of Operations Research, 2001,53 (2) : 233 - 245.
  • 9JING Liu, WEN Song. On proper efficiencies in locally convex spaces-a survey[J]. Acta Mathematica Vietnamica, 2001, 26(3) :301 - 312.
  • 10ZHENG X Y. Proper efficiency in locally convex topological vector spaces EJ 1. Journal on Control and Optimization, 1977, 94(2) :469 - 486.

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系统科学与数学
2003年 第4期

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