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锥约束多目标规划的二阶对称对偶性质(英文) 被引量：3

Second-order Symmetric Duality for a Multiobjective Programming Problem with Cone Constraints
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摘要 给出一对锥约束多目标非线性规划的二阶对称对偶问题,以及二阶F凸函数类的概念.在二阶F凸假设下证明了真有效解的对偶性质———弱对偶性、强对偶性及逆对偶性. A pair of second order symmetric dual problems in multiobjective nonlinear programming with cone constraints is formulated, and the definitions of a class of second-order F- convex functions are introduced, Then, under the second-order F- convex assumptions, dual theorems （weak duality, strong duality and converse duality） related to the properly efficient solution are proved,
作者 陈秀宏
机构地区 淮阴师范学院数学系
出处 《应用数学》 CSCD 北大核心 2006年第1期127-133,共7页 Mathematica Applicata
基金 SupportedbytheNaturalScienceFoundationofJiangsuHighSchool(03KJB110012)andJiangsuEducationOffice(00KJD110001,01KJD110005)
关键词 多目标规划 二阶对称规划 锥约束 真有效解 二阶F-凸性 对偶定理 Multiobjective program Second-order symmetric programs Cone constraint Properly efficient solution Second-order F- convexity Duality theorems
分类号 O224 [理学—运筹学与控制论]
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参考文献10

  • 1Devi G. Symmetric duality for nonlinear programming problem involving η- bonvex functions[J]. European Journal of Operational Research, 1998,104:615 - 621.
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同被引文献14

  • 1杨新民.两类非线性规划的对称对偶性[J].重庆师范学院学报（自然科学版）,1993,10(2):5-8. 被引量：1
  • 2Mishra S K.Second order symmetric duality in mathematical programming with F- convexity[J]. European Journal of Operational Research,2000,127:506 - 518.
  • 3Fritz, John, Extremum problems with inequalities as side conditions, in: Studies and Essays, Courant Anniversary Volume, K. O. Friedrichs, O. E. Neugenbauer, and J. J. Stoker(eds. ), hterscience, New York, 1968,187 - 204.
  • 4Dantzing G B, Eisenberg E and Cottle R W. Symmetric dual nonlinear programs[ J]. Pacific J Math, 1965,15,809- 812.
  • 5Mond B. A symmetric dual theorem for nonlinear programs[ J]. Quart Appl Math, 1965,23,265 - 269.
  • 6Bazaraa M S, Goode J J. On symmetric duality in nonlinear programming[ J ]. Operation Research, 1973,21,1 - 9.
  • 7Mond B, Weir T. Generalized concavity and duality, in "Generalized Concavity in Optimization and Economics" [ M]. New York: Academic Press, 1981,263 - 279.
  • 8Dantzig G B,Eisenberg E,Cottle R W. Symmetric dual nonlinear programs[J].Pacific Journal of Mathematics,1965.809-812.
  • 9Mond B,Weir T. Symmetric duality for nonlinear muhiobjective programming[A].London:Gordon and Breach,1997.137-153.
  • 10Bazaraa M S,Goode J J. On symmetric duality in nonlinear programming[J].Operations Research,1973.1-9.

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应用数学
2006年 第1期

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