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 混合型对偶
 mixed type dual
 Mixed type dual for generalized fractional programming 广义分式规划的混合型对偶 短句来源 In this paper, we give a mixed type dual problem for a class of nondifferentiable generalized fractional programming problems with the norm \\$‖Bx‖\-p\\$ in the objective function involves, and present weak duality, strong duality, and strict converse duality theorems under the assumptions of generalized \\$(F, ρ)\|\\$convexity. 对一类目标函数含范数‖ Bx‖p 的非可微广义分式规划 ,提出了一个混合型对偶 ,并且在广义 (F,ρ) -凸性条件下 ,给出了相应的弱对偶定理、强对偶定理及严格逆对偶定理 短句来源 In Section 5, Mond-Weir type dual and Wolfe type dual are introduced and the mixed type dual proposed by Xu Zengkun is discussed. 第五节介绍了Mond-Weir对偶和Wolfe对偶，并重点讨论了徐增坤教授提出的混合型对偶。 短句来源 A MIXED TYPE DUAL FOR GENERALIZDE FRACTIONAL PROGRAMMING 广义分式规划的一个混合型对偶 短句来源 This paper gives one mixed type dual problem for a class of nondifferentiable generalized fractional programmingproblems, and proves weak duality, strong duality, and strict converse duality theorems under the assumptions of generalized(F,ρ) -convexity. 给出了一类非可微广义分式规划的一个混合型对偶。 在广义(F、ρ)-凸性条件下,证明了弱对偶定理、强对偶定理及严格逆对偶定理。 短句来源 更多
 mixed dual
 Mixed Dual for Generalized Fractional Programming with (F,α,ρ,d)-Convexity 具有(F,α,ρ,d)-凸广义分式规划的混合型对偶 短句来源 In this paper,we give the mixed dual problem a class of generalized fractional programming,and present weak duality,strong duality,and strict converse duality theorems under the assumption of (F,α,ρ,d)- convexity. 对于一类目标函数中有无限个分式的广义分式规划,给出了一个混合型对偶,并在(F,α,ρ,d)-凸性的条件下,证明了相应的弱对偶定理、强对偶定理及严格逆对偶定理. 短句来源
 mixed type duality
 Mixed type duality for a class of nondifferentiable generalized fractional programming 一类非可微广义分式规划的混合型对偶 短句来源
 mixed duality
 A Mixed Duality for A Class of Generalized Convex Multiobjective Control Problems 一类广义凸多目标控制问题的混合型对偶 短句来源

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 mixed type dual
 Several duality theorems concerning weak, strong, and strict converse duality under the framework in mixed type dual form are proved.
 mixed dual
 We present as examples of application: the Dirichlet problem for the Laplace operator, in mixed dual formulation, with and without numerical integration. In addition, we formulate a mixed dual problem corresponding to primal problem, and discuss weak, strong and strict converse duality theorems. By Lemma 2.3, this amounts since Xq is shift-invariant to showing that the mixed dual Gramian eG of RXq;Xq is the identity a.e. In this publication, it is shown that the same model fails to predict combustion for partially pre mixed dual-fuel engines. Several properties of the mixed dual Gramian can be proved by carefully modifying the proofs of corresponding results of the dual Gramian. 更多
 Non-smooth programming problems with invexity of the form(P) minf(x),s.t. g(x)0are considered, where f: Rn→R,g: Rn→Rm, and fj, gi are locally Lipschitz at certain points. The necessary and sufficient optimality conditions on problems(P) are presented. A mixed type dual on (P) is proposed,which is a generalization of known Wolfe type and Mond-Weir type dual,and the weak duality and strong duality are obtained. Finally,multiobjective non-smooth programming problems with invexity are also investigated,and similar... Non-smooth programming problems with invexity of the form(P) minf(x),s.t. g(x)0are considered, where f: Rn→R,g: Rn→Rm, and fj, gi are locally Lipschitz at certain points. The necessary and sufficient optimality conditions on problems(P) are presented. A mixed type dual on (P) is proposed,which is a generalization of known Wolfe type and Mond-Weir type dual,and the weak duality and strong duality are obtained. Finally,multiobjective non-smooth programming problems with invexity are also investigated,and similar results are formulated. 研究下述非光滑不变凸规划问题（Ｐ）ｍｉｎｆ（ｘ），ｓ．ｔ．ｇ（ｘ）０这里ｆ：Ｒｎ→Ｒ，ｇ：Ｒｎ→Ｒｍ．ｆｊ，ｇｉ为不变凸函数，在相关点具有Ｌｉｐｓｃｈｉｔｚ性质．将要给出最优性的必要与充分条件．同时提出（Ｐ）的混合型对偶问题，它们是经典的Ｗｏｌｆｅ型对偶和Ｍｏｎｄ－Ｗｅｉｒ型对偶的推广，给出弱对偶和强对偶结果．最后，考察多目标非光滑不变凸规划问题且得到类似的结果． For multiobjective mathematical programming, the authors proposed a mixed type dual.Wolfe type dual and Mond-Weir type dual are its special cases, Then, gave a generalization of nonhomogeneous Farkas' lemma, by which a necessary and sufficient condition is obtained for weak duality between the primal and the dual. 对于可微的多目标数学规划，提出了一种混合型对偶；Wolfe式对偶和Mond－Weir式对偶是它的特例。接着给出了非齐次Farkas引理的一种推广。利用它可得出与弱有效解概念有关的弱对偶成立的充要条件。 Sufficient condition and mixed type dual were pr esented for the generalized fractional programming under (F,ρ)-convexity a ssumptions. The results about weak duality, strong duality and strictly reverse duality were also obtained under more suitable conditions. 在函数 (F ,ρ) 凸性假设下 ,给出了广义分式规划的最优性充分条件及其混合型对偶 ,并且在适当的条件下 ,给出了相应的弱对偶定理、强对偶定理 ,以及严格逆对偶定理 . << 更多相关文摘
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