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        具有廣義C-凸性的一類分式規(guī)劃的對偶

        2020-04-12 00:00:00李鈺嚴(yán)建軍李江榮

        3 結(jié)語

        本文在已有文獻(xiàn)提出的新廣義凸性概念基礎(chǔ)上,針對包含此類廣義凸性的分式規(guī)劃的對偶問題進(jìn)行了探討,得到的結(jié)果豐富了廣義凸性和最優(yōu)化的有關(guān)理論,可進(jìn)一步研究其Wolfe型對偶性、鞍點(diǎn)等內(nèi)容。

        參考文獻(xiàn):

        [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 amp; 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]嚴(yán)建軍, 李鈺, 李江榮. 關(guān)于一類多目標(biāo)半無限分式規(guī)劃的最優(yōu)性條件[J]. 重慶理工大學(xué)學(xué)報(自然科學(xué)), 2018,32(12):205-210.

        [8]嚴(yán)建軍, 李鈺, 楊帆,等. 關(guān)于一類多目標(biāo)半無限規(guī)劃的最優(yōu)性條件[J]. 貴州大學(xué)學(xué)報(自然科學(xué)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.

        (責(zé)任編輯:周曉南)

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