共查询到18条相似文献,搜索用时 62 毫秒
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本文利用Dini右上、右下导数给出了非光滑伪线性多目标规划的对偶理论,建立了Mond-Weir型对仍与Wolf型对偶;并证明了原问题与对偶问题之间的对偶定理. 相似文献
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本文在集值优化的框架下提出了一个二层多目标规划模型(BLMOP).利用集值映射的相依导数和相依上导数,给出了几个有关(BLMOP)的弱有效解的必要或充分最优性条件. 相似文献
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In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them. 相似文献
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周轩伟 《高校应用数学学报(A辑)》2016,(1):63-72
研究了一类非光滑多目标规划问题.这类多目标规划问题的目标函数为锥凸函数与可微函数之和,其约束条件是Euclidean空间中的锥约束.在满足广义Abadie约束规格下,利用广义Farkas引理和多目标函数标量化,给出了这一类多目标规划问题的锥弱有效解最优性必要条件. 相似文献
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利用K-方向导数,给出了一类存在性更为广泛的广义凸函数.即广义一致K-(F,α,ρ,d)-I型凸函数,进而讨论了涉及这些新广义凸性的一类多目标半无限规划的最优性条件。 相似文献
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曾韧英 《数学物理学报(A辑)》1999,(Z1)
该文对定义于局部凸线性拓扑空间X上的泛函引入广义方向导数、广义梯度及满足Lips-chitz条件等概念,证明了它们的几个重要性质,并举例说明这里满足Lipschitz条件的概念是Ba-nach空间情形的严格推广.最后,作为上述结论及方法的应用,讨论定义于X的多目标数学规划,得出若干关于弱有效解的最优性条件. 相似文献
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本文讨论了集函数多目标(分母不同)分式规划,给出了Geoffrion正常有效解的必要和充分条件,并讨论了关于有效解的广义凸对偶理论. 相似文献
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非光滑多目标规划的最优性条件 总被引:8,自引:0,他引:8
近年来,关于非光滑最优化问题的研究十分活跃,尤其是对单目标规划,出现了很多成果.关于非光滑多目标规划,也有不少工作.然而,以前的研究,多是利用次微分(凸规划情形)或广义梯度进行讨论的.文[1]利用古典方向导数给出了非光滑无约束单目标规划的最优性条件,并指出,在广泛的非光滑函数类中,方向导数是存在的.本文则以更 相似文献
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This paper is concerned with second-order duality for a class of nondifferentiable multiobjective programming problems. Usual duality theorems are proved for Mangasarian type and general Mond–Weir type vector duals under generalized bonvexity assumptions. 相似文献
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In this paper, three sufficient conditions are given, one of which modifies the previous result given by Singh (Ref. 1) under the assumption of convexity of the functions involved at the Pareto-optimal solution. A counterexample has been furnished which shows that the convexity assumption cannot be extended to include the quasiconvexity case. The second theorem on sufficiency requires the strict pseudoconvexity of the functions involved. 相似文献
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Optimality and Duality in Nondifferentiable and Multiobjective Programming under Generalized d-Invexity 总被引:1,自引:1,他引:0
In this paper, we are concerned with the nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized d-type-I functions. By utilizing the new concepts, Antczak type Karush-Kuhn-Tucker sufficient optimality conditions, Mond-Weir type and general Mond-Weir type duality results are obtained for non-differentiable and multiobjective programming. 相似文献
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D. S. Kim S. J. Kim PhD Student M. H. Kim 《Journal of Optimization Theory and Applications》2006,129(1):131-146
In this paper, we consider a class of nondifferentiable multiobjective fractional programs in which each component of the
objective function contains a term involving the support function of a compact convex set. We establish necessary and sufficient
optimality conditions and duality results for weakly efficient solutions of nondifferentiable multiobjective fractional programming
problems.
This work was supported by Grant R01-2003-000-10825-0 from the Basic Research Program of KOSEF. 相似文献
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We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving
(F, α, ρ, d)-convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate
duality theorems.
The authors thank the referee for valuable suggestions improving the presentation of the paper. 相似文献
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本文主要从多目标规划相应的加权问题出发,讨论了在ε-次可微的条件下,凸多目标规划问题η-有效解存在的必要条件与充分条件. 相似文献
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I. Ahmad Z. Husain Sarita Sharma 《Numerical Functional Analysis & Optimization》2013,34(9-10):989-1002
A new generalized class of higher-order (F, α, ρ, d)–type I functions is introduced, and a general Mond–Weir type higher-order dual is formulated for a nondifferentiable multiobjective programming problem. Based on the concepts introduced, various higher-order duality results are established. At the end, some special cases are also discussed. 相似文献
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B. Jiménez 《Journal of Optimization Theory and Applications》2003,116(1):99-116
In this paper, sufficient conditions for superstrict minima of order m to nondifferentiable multiobjective optimization problems with an arbitrary feasible set are provided. These conditions are expressed through the Studniarski derivative of higher order. If the objective function is Hadamard differentiable, a characterization for strict minimality of order 1 (which coincides with superstrict minimality in this case) is obtained. 相似文献