共查询到19条相似文献,搜索用时 480 毫秒
1.
本文考虑了Farkas引理,Gordan引理及其拓展形式之间的关系,从理论上证明了其等价性并说明了Farkas引理在各种等价形式中的重要地位,并指出了Gordan引理实际是叮看作是Farkas引理的弱形式,然后研究了Farkas引理及其它形式在锥线性不等式组中的推广. 相似文献
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该文主要研究一类目标函数和约束函数均具有谱面不确定数据的两阶段自适应鲁棒多目标规划问题.首先,建立具有仿射自适应变量的两阶段自适应鲁棒多目标规划问题的Farkas引理.随后,引入该多目标规划问题的半定规划对偶问题.最后,借助该Farkas引理,刻画它们之间的对偶性质. 相似文献
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《数学物理学报(A辑)》2018,(5)
借助Dinkelbach的方法(见文献[1]),将带复合函数的分式优化问题转化为约束优化问题,通过引入新的约束规范条件,建立了约束优化问题的对偶理论,进而刻画了带复合殿数的分式优化问题的Farkas类引理. 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
6.
特征数≠2的非交换主理想整环上线性群的自同构 总被引:1,自引:0,他引:1
<正> 华罗庚和J.Dieudonné研究了体上线性群的自同构问题,而华罗庚和Ⅰ.Reiner以及作者则研究了整数环上线性群的自同构问题.因为整数环是一种特殊的环,所以一般体上线性群的自同构的结果不能从整数环上线性群的自同构的结果导 相似文献
7.
非整边的直角三角形整距点问题 总被引:2,自引:2,他引:0
以直角顶点为原点 ,两直角边分别为 x轴和 y轴的正方向建立坐标系 .不妨设斜边所在直线方程为 ax +by=n,则方程 ax +by=n - kc(其中 a、b、c∈ N+,且 a2 +b2 =c2 ,k为整数 )的正整数解就是整距点的坐标 ,因此整距点问题与一类不定方程的正整数解联系起来 .设 a,b,n皆为正整数 ,有以下引理 .引理 1 方程 ax +by =n有整数解的充要条件是 (a,b) |n.引理 2 若 (a,b) =1,且 x0 ,y0 为方程 ax+by =n的一组解 ,则方程其它解可表示为 :x =x0 +bt,y =y0 - at(t为整数 ) .引理 3 设 (a,b) =1,则当 n>ab- a-b时 ,方程 ax +by =n必有非负整数解 .以… 相似文献
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主要目的是利用Liouville反转公式来给出整数素因数间的一个新的对偶公式,从而推广了K.Alladi的基于Mbius反转公式的对偶引理. 相似文献
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p-除环上矩阵的广义逆 总被引:10,自引:0,他引:10
<正> 广义逆矩阵理论最近分别被推广到域上与有限域上.本文将讨论p-除环上矩阵的广义逆.我们要用到下面的 引理1 设A是除环△上矩阵的r×r可逆子阵,则 相似文献
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In this paper, we present versions of the Farkas Lemma and the Gale Lemma for a semi-infinite system involving positively homogeneous functions in a topological vector space. In particular, we present two such versions for a semi-infinite system containing min-type functions. Our main theoretical tool is abstract convexity. 相似文献
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S. S. Kutateladze 《Siberian Mathematical Journal》2010,51(1):78-87
Boolean valued analysis is applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous
linear inequalities. 相似文献
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David Bartl 《Linear and Multilinear Algebra》2013,61(8):897-901
The author published ‘A Short Algebraic Proof of the Farkas Lemma’ [SIAM J. Optim. 19 (2008), pp. 234–239]. The author then found, in his opinion, a better exposition of the proof. He would therefore like to publish the new form of the proof in this note. 相似文献
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Stephen A. Clark 《Positivity》2006,10(3):475-489
The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological
generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive
cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional
extension of the Theorem of the Alternative. 相似文献
15.
A MINIMUM-RATIO-TEST-FREE APPROACH TO LINEAR PROGRAMMING 总被引:1,自引:1,他引:0
Wang Zhemin 《数学年刊B辑(英文版)》1989,10(4):472-479
16.
《Operations Research Letters》2020,48(3):329-335
Farkas’ Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested procedure to construct a function that characterizes feasibility over right-hand sides and can determine which statement in a theorem of the alternative holds. 相似文献
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David Bartl 《Mathematical Methods of Operations Research》2012,75(1):101-104
We present a very short algebraic proof of a generalisation of the Farkas Lemma: we set it in a vector space of finite or
infinite dimension over a linearly ordered (possibly skew) field; the non-positivity of a finite homogeneous system of linear
inequalities implies the non-positivity of a linear mapping whose image space is another linearly ordered vector space. In
conclusion, we briefly discuss other algebraic proofs of the result, its special cases and related results. 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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Any linear (ordinary or semi-infinite) optimization problem, and also its dual problem, can be classified as either inconsistent or bounded or unbounded, giving rise to nine duality states, three of them being precluded by the weak duality theorem. The remaining six duality states are possible in linear semi-infinite programming whereas two of them are precluded in linear programming as a consequence of the existence theorem and the non-homogeneous Farkas Lemma. This paper characterizes the linear programs and the continuous linear semi-infinite programs whose duality state is preserved by sufficiently small perturbations of all the data. Moreover, it shows that almost all linear programs satisfy this stability property. 相似文献