(V,η)-I型对称不变凸多目标规划的对偶性

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英文篇名：Duality in multiobjective programming under (V, η)-type Ⅰ symmetrical invexity 作者：王雪峰 ; 王芮婕 ; 高晓艳 英文作者：WANG Xue-feng;WANG Rui-jie;GAO Xiao-yan;College of Science, Xi'an University of Science and Technology; 关键词：(V ; η)-Ⅰ型对称不变凸函数 ; 多目标规划 ; 对称梯度 ; 对偶性 英文关键词：(V,η)-type symmetrical invex function;;multiobjective programming;;symmetrical gradient;;duality 中文刊名：SDDX 英文刊名：Journal of Shandong University(Natural Science) 机构：西安科技大学理学院; 出版日期：2019-03-26 08:51 出版单位：山东大学学报(理学版) 年：2019 期：v.54 基金：陕西省自然科学研究计划项目(2017JM1041);; 陕西省教育厅专项科研计划项目(15JK1456) 语种：中文; 页：SDDX201904017 页数：11 CN：04 ISSN：37-1389/N 分类号：120-130

摘要

利用对称梯度,定义了一类新的广义不变凸函数:(V,η)-Ⅰ型对称不变凸函数、(V,η)-Ⅰ型对称严格拟不变凸函数以及(V,η)-Ⅰ型对称严格拟伪不变凸函数,并在新广义凸性的假设下,研究了一类多目标规划问题的Mond-Weir型对偶,得到了这类多目标规划的若干个弱对偶定理、强对偶定理以及严格逆对偶定理。
        By using symmetrical gradient, a class of new generalized invex function,(V, η)-type Ⅰ symmetrical invex function,(V, η)-type Ⅰ strictly symmetrical quasi invex function and(V, η)-type Ⅰ strictly symmetrical quasiqseudo invex function are defined. Under the new generalized invexity, the Mond-Weir dual model in a class of multi-objective programming problem is discussed, and several weak duality results, strong duality result and strict converse duality result are obtained.

引文

[1] MANDAL P, NAHAK C. Symmetric duality with (p, r)-ρ-(η, θ)-invexity[J]. Applied Mathematics and Computation, 2011, 217(21):8141-8148.
    [2] TRIPATHY A K, DEVI G. Wolfe type higher order multiple objective nondifferentiable symmetric dual programming with generalized invex function[J]. Journal of Mathematical Modelling and Algorithms in Operations Research, 2014, 13(4):557-577.
    [3] 卢厚佐, 高英. 多目标分式规划逆对偶研究[J]. 数学的实践与认识, 2014, 44(23):172-178.LU Houzuo, GAO Ying. Converse duality for multiobjective fractional programming[J]. Mathematics in Practice and Theory, 2014, 44(23):172-178.
    [4] BHATIA D, MEHRA A. Lagrange duality in multiobjective fractional programming problems with n-set functions[J]. Journal of Mathematical Analysis and Applications, 1999, 236(2):300-311.
    [5] GAO X Y. Optimality and duality for non-smooth multiple objective semi-infinite programming[J]. Journal of Networks, 2013, 8(2):413-420.
    [6] GUPTA S K, KAILEY N. Second-order multiobjective symmetric duality involving cone-bonvex functions[J]. Journal of Global Optimization, 2013, 55(1):125-140.
    [7] HACHIMI M, AGHEZZAF B. Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions[J]. Journal of Mathematical Analysis and Applications, 2004, 296(2):382-392.
    [8] HANSON M A, RITA P N, SINGH C. Multiobjective programming under generalized type i invexity[J]. Journal of Mathematical Analysis and Applications, 2001, 261(2):562-577.
    [9] GAO Xiaoyan. Two duality problems for a class of multiobjective fractional programming[J]. Computer Modelling & New Technologies, 2014, 18(10):151-157.
    [10] GAO X Y. Second order duality in multiobjective programming with generalized convexity[J]. International Journal of Grid and Distributed Computing, 2014, 7(5):159-170.
    [11] 赵洁. 一类不可微多目标规划的Mond-Weir型对偶[J]. 重庆师范大学学报(自然科学版), 2017, 34(3):1-5.ZHAO Jie. Mond-weir duality for a class of nondifferentiable multiobjective programming[J]. Journal of Chongqing Normal University(Natural Science), 2017, 34(3):1-5.
    [12] 张庆祥. 一类广义I类不变凸半无限规划的对偶性[J]. 延安大学学报(自然科学版), 2003, 22(4):6-8.ZHANG Qingxiang. Duality for a class of semi-infinite programming under generalized type-I invexity[J]. Journal of Yan?an University(Natural Science Edition), 2003, 22(4):6-8.
    [13] 杨勇. Iε类半无限规划的最优性条件[J]. 西南师范大学学报(自然科学版), 2014, 39(3):45-48.YANG Yong. On optimality conditions for semi-infinite programming with type-Iε convexity[J]. Journal of Southwest China Normal University (Natural Science Edition), 2014, 39(3):45-48.