共查询到20条相似文献,搜索用时 62 毫秒
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本文讨论F—广义凸多目标规划的对偶理论,证明了弱对偶、直接对偶和逆对偶定理.主要结果参考文献[1]的推广和发展。 相似文献
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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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在有效解的意义下,对一类含有BF—I函数的多目标变分问题给出了混合型对偶的强对偶定理、弱对偶定理和严格逆对偶定理。 相似文献
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本文讨论无限维向量最优化问题的Lagrange对偶与弱对偶,建立了若干鞍点定理与弱鞍点定理.作为研究对偶问题的工具,建立了一个新的择一定理. 相似文献
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在I型弧连通和广义I型弧连通假设下,建立了极大极小分式优化问题的对偶模型,并提出了弱对偶定理、强对偶定理和严格逆对偶定理. 相似文献
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Georgi D. Dimov 《Applied Categorical Structures》2009,17(5):501-516
Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of locally compact
Hausdorff spaces and perfect maps. 相似文献
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《Linear and Multilinear Algebra》2007,55(4):327-353
We briefly consider several formulations of Farkas' Lemma first. Then we assume the setting of two vector spaces, one of them being linearly ordered, over a linearly ordered field till the end of this article. In this setting, we state a generalized version of Farkas' Lemma and prove it in a purely linear-algebraic way. Afterwards, we present Theorems of Motzkin, Tucker, Carver, Dax, and some other theorems of the alternative that characterize consistency of a finite system of linear inequalities. We also mention the Key Theorem, which is a related result. Finally, we use Farkas' Lemma to prove the Duality Theorem for linear programming (with a finite number of linear constraints). The Duality Theorem that is proved here covers, among others, linear programming in a real vector space of finite or infinite dimension and lexicographic linear programming. 相似文献
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We give a duality for the variety of bounded distributive lattices that is not full (and therefore not strong) although it
is full but not strong at the finite level. While this does not give a complete solution to the “Full vs Strong” Problem,
which dates back to the beginnings of natural duality theory in 1980, it does solve it at the finite level. One consequence
of this result is that although there is a Duality Compactness Theorem, which says that if an alter ego of finite type yields
a duality at the finite level then it yields a duality, there cannot be a corresponding Full Duality Compactness Theorem.
Received October 1, 2002; accepted in final form November 10, 2004. 相似文献
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Nontrivial solutions for elliptic resonant problems are obtained via Morse theory. To compute the critical groups at infinity of the relevant functional, we propose a new approach by combining the homotopy and reduction methods, and the Alexander Duality Theorem. 相似文献
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Christopher Heil 《Journal of Fourier Analysis and Applications》2007,13(2):113-166
The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis. This expository survey
attempts to reconstruct the long and very involved history of this theorem and to present its context and evolution, from
the one-dimensional rectangular lattice setting, to arbitrary lattices in higher dimensions, to irregular Gabor frames, and
most recently beyond the setting of Gabor frames to abstract localized frames. Related fundamental principles in Gabor analysis
are also surveyed, including the Wexler-Raz biorthogonality relations, the Duality Principle, the Balian-Low Theorem, the
Walnut and Janssen representations, and the Homogeneous Approximation Property. An extended bibliography is included. 相似文献
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H Paul Williams 《The Journal of the Operational Research Society》2016,67(3):450-456
The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier–Motzkin Elimination. It is also explained how redundant inequalities can be removed, using the method attributed to Chernikov and to Kohler. Some new results are given. The procedure also leads to a transparent explanation of Farkas’ Lemma, LP Duality, the dual form of Caratheodory’s Theorem as well as generating all vertices and extreme rays of the Dual Polytope. 相似文献
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《European Journal of Operational Research》1988,33(3):342-348
This paper studies the applications of lexicographical order relation for vectors in the mathematical theory of multiobjective programming. We show that any Pareto minimum of an unconstrained convex. problem is the lexicographical minimum for the problem associated to a matrix multiplier having lexicographical positive columns. A similar result is also obtained for inequality constrained problems.Our approach to the theory of duality follows the pattern of Jahn [3], but we substitute vectors by matrices in the formulation of the dual problem and the usual scalar order relation by the lexicographical order relation. This allows us to state the Strong Duality Theorem in terms of Pareto minima and to eliminate some regularity assumptions. 相似文献
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S. Simons 《Transactions of the American Mathematical Society》1998,350(7):2953-2972
In this paper, we derive sufficient conditions for the sum of two or more maximal monotone operators on a reflexive Banach space to be maximal monotone, and we achieve this without any renorming theorems or fixed-point-related concepts. In the course of this, we will develop a generalization of the uniform boundedness theorem for (possibly nonreflexive) Banach spaces. We will apply this to obtain the Fenchel Duality Theorem for the sum of two or more proper, convex lower semicontinuous functions under the appropriate constraint qualifications, and also to obtain additional results on the relation between the effective domains of such functions and the domains of their subdifferentials. The other main tool that we use is a standard minimax theorem.
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