非光滑多目标分式规划的对偶条件

doi:10.3785/j.issn.1008-9497.2016.06.011

摘要
图/表
参考文献
相关文章 (1)

全文: PDF (500 KB) HTML( )
输出: BibTeX | EndNote (RIS)

摘要最优性问题在研究博弈理论、目标规划、最低风险问题等方面有重要应用，利用非光滑分析，定义了一类新的广义不变凸函数，研究了涉及此类函数的多目标半无限分式规划问题，得到了参数对偶问题的弱对偶和严格逆对偶条件，在新的凸性下得到了一些重要结论.

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	李向有

关键词 ：广义不变凸函数, 多目标, 对偶, 分式规划

Abstract：Optimization plays an important role in game theory, goal programming, minimum risk problems, etc. By nonsmooth analysis, a new class of invex functions are defined, and multi-objective semi-infinite fractional programming problems involving the new defined invex functions are investigated. Then, weak dual conditions and strictly converse dual conditions of parameter dual problems are obtained, and some important conclusions are also drawn under the new convexity.

Key words： generalized invex functions multiobjective duality fractional programming

收稿日期: 2015-08-22

ZTFLH:	O221.6
	O224

基金资助:国家自然科学基金资助项目(11471007)；陕西省教育厅科研项目资助课题(14JK1840).

作者简介: 李向有(1976-),ORCID:http://orcid.org/0000-0002-3761-1118,男,硕士,副教授,主要从事最优化理论与应用研究,E-mail:yadxlxy@163.com.

引用本文:

李向有. 非光滑多目标分式规划的对偶条件[J]. 浙江大学学报（理学版）, 2016, 43(6): 682-684.
LI Xiangyou. Duality conditions of nonsmooth multi-objective fractional programming. Journal of ZheJIang University(Science Edition), 2016, 43(6): 682-684.

链接本文:

http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.06.011 或 http://www.zjujournals.com/sci/CN/Y2016/V43/I6/682

[1] ANTCZAK T. A class of B-(p,r) invex functions and mathematical programming[J]. J Math Anal Appl,2003,286:187-206.
[2] ZHANG Y, ZHU B, XU Y T. A class of Lipschitz B-(p,r)-invex functions and nonsmooth programming[J]. OR Transactions,2009,13(1):61-71.
[3] ANTCZAK T, SINGH V. Generalized B-(p,r)-invexity functions and nonlinear mathematical programming[J]. Numercial Functional Analysis and Optimization,2009,30:1-22.
[4] 万轩,彭再云.B-(p,r)-预不变凸规划的Mond-weil对偶问题研究[J].重庆师范大学学报,2011,28(1):1-7. WAN Xuan, PENG Zaiyun.The research of mond-weir duality for programming with B-(p,r)-preinvexity function[J]. Journal of Chongqing Normal University,2011,28(1):1-7.
[5] ANTCZAK T. Generalized fractional minimax programming with B-(p,r)-invexity[J]. Computer and Mathematics with Applications,2008,56:1505-1525.
[6] 李向有,张庆祥.广义I型函数的对偶性条件[J].贵州大学学报,2014,31(2):22-24. LI Xiangyou, ZHANG Qingxiang.Dual conditions of generalized I type functions[J]. Journal of Guizhou University,2014,31(2):22-24.
[7] ANTCZAK T, SINGH V. Optimality and duality for minimax fractional programming with support function under B-(p,r)-Type I assumptions[J]. Mathematical and Computer Modelling,2013,57(S5/6):1083-1100.
[8] JAYSWAL A, PRASAD A K, STANCU-MINASIAN I M. On nonsmooth multiobjective fractional programming problems involving(p,r)-ρ-(η,θ) invex functions[J]. Yugoslav Journal of Operations Research,2013,23:367-386.
[9] MISHRA S K, LAI K K, SINGH V. Optimality and duality for minimax fractional programming with support function under(c,α,ρ,d)-convexity[J]. Journal of Computional and Applied Mathematics,2015,274:1-10.
[10] GUPTA R, SRIVASTAVA M. Optimality and duality for nonsmooth multiobjective programming using G-type I functions[J].Applied Mathematics and Compution,2014,240(4):294-307.
[11] CLARKE F H. Optimization and Nonsmooth Analysis[M]. New York:Wiley-Interscience,1983.
[12] KUK H, LEE G M, TANINO T. Optimality and duality for nonsmooth multiobjective fractional programming with generalized invexity[J]. Journal of Mathematical Analysis and Applications,2001,262(1):365-375.