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具有广义C-凸性的一类分式规划的对偶

2020-06-08李钰严建军李江荣

关键词:对偶广义分式

李钰 严建军 李江荣

3 结语

本文在已有文献提出的新广义凸性概念基础上,针对包含此类广义凸性的分式规划的对偶问题进行了探讨,得到的结果丰富了广义凸性和最优化的有關理论,可进一步研究其Wolfe型对偶性、鞍点等内容。

参考文献:

[1]YUAN D H, LIU X L, CHINCHULUUN A, et al. Nondifferentiable minimax fractional programming problems with (C,α,ρ,d)-convexity [J]. Journal of Optimization Theory and Application,2006,129(1):185-199.

[2]CHINCHULUUN A, PARDALOS P M. Multiobjective programming problems under generalized convexity[M]//TRN A, ILINSKAS  J. Models and Algorithms for Global Optimization. New York:Springer,2007:3-20.

[3]CHINCHULUUN A, YUAN D H, PARDALOS P M. Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity[J].Annals of Operations Research,2007,154(1):133-147.

[4]YUAN D H, CHINCHULUUN A, LIU X L, et al. Generalized Convexities and generalized gradients based on algebraic operations[J]. Journal of Mathematical Analysis and Applications,2006,321(2):675-690.

[5]YUAN D H, CHINCHULUUN A, LIU X L, et al. Optimality conditions and duality for multiobjective programming involving (C,α,ρ,d)-type-I functions[M]//KONNOV I V, LUC D T, RUBINOV A M. Lecture Notes in Economics & Mathematical Systems:Generalized Convexity and Related Topics. Berlin: Springer-Verlag, 2007:73-87.

[6]LONG X J. Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with (C,α,ρ,d)-convexity[J]. Journal of Optimization Theory and Application,2011,148(1):197-208.

[7]严建军, 李钰, 李江荣. 关于一类多目标半无限分式规划的最优性条件[J]. 重庆理工大学学报(自然科学), 2018,32(12):205-210.

[8]严建军, 李钰, 杨帆,等. 关于一类多目标半无限规划的最优性条件[J]. 贵州大学学报(自然科学版), 2019,36(2):16-20.

[9]KANZI N. Necessary and sufficient conditions for (weakly) efficient of non-differentiable multi-objective semi-infinite programming problems[J]. Iranian Journal of Science and Technology, Transactions A: Science,2018,42(3):1537-1544.

[10]CHUONG T D, KIM D S. Nonsmooth semi-infinite multiobjective optimization problems[J]. Journal of Optimization Theory and Applications, 2014,160(3):748-762.

(责任编辑:周晓南)

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