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On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory 总被引:1,自引:0,他引:1
J. B. G. Frenk P. Kas G. Kassay 《Journal of Optimization Theory and Applications》2007,132(3):423-439
In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming
duality and the finite intersection property for compact sets. It turns out that these necessary and sufficient conditions
have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions
for strong duality for a general class of optimization problems.
The authors like to thank the comments of the anonymous referees for their remarks, which greatly improved the presentation
of this paper. 相似文献
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We establish the necessary and sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions. Subsequently, we apply the optimality conditions to formulate one parametric dual problem and we prove weak duality, strong duality, and strict converse duality theorems. 相似文献
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利用有限维线性空间的理论,研究了一类无限阶Toeplitz矩阵的特征值问题,得到这类无限阶矩阵的特征值是连续变化的,并且其谱集合是由复平面上的单位圆盘{z∈C,|z|<1}被多项式函数f(z)=(?)a_iz~i作用后,所得到的像曲线内部的点组成. 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
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本文利用无穷下降方向,在Banach空间中建立了若干非凸对偶规划的存在性定理。作为特例,给出了半无限对偶规划和有限对偶规划的存在性定理。 相似文献
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唐建国 《数学的实践与认识》2006,36(4):135-143
为使线性规划的每个约束条件部分或全部地拥有原整个约束条件所包含的信息,将线性规划的约束条件“滚雪球”后得到与原约束条件等价的新约束条件,对新约束条件所构成的线性规划采用目标函数最速递减算法.有一定规模的随机数值算例显示了该算法只需进行m(约束条件数)次迭代即可求得最优解. 相似文献
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Ching-Feng Wen 《Numerical Functional Analysis & Optimization》2013,34(1):80-129
This article proposes a practical computational procedure to solve a class of continuous-time linear fractional programming problems by designing a discretized problem. Using the optimal solutions of proposed discretized problems, we construct a sequence of feasible solutions of continuous-time linear fractional programming problem and show that there exists a subsequence that converges weakly to a desired optimal solution. We also establish an estimate of the error bound. Finally, we provide two numerical examples to demonstrate the usefulness of this practical algorithm. 相似文献
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一类奇异非线性方程的正整体解存在的充分必要条件 总被引:2,自引:0,他引:2
本文研究形如Δ^nu=f(|x|,u,|Δ↓u|u^-β,x∈R^N的奇异非线性多调和方程在R^N(N≥3)上的正整体解,给出了该方程具有无穷多个其渐进阶刚好为|x|^2n-2的正整体解的充分与必要条件。 相似文献
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本文引进了一种可调参数的方法,应用该方法研究了线性微分差分系统的渐近稳定性,得到了该系统渐近稳定性的充要条件的代数判别准则. 相似文献
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The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraintis proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. optimal control, maximum principle, distributed parameter system, linear system,vector-valued measure. 相似文献
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证明了闭的极大线性子空间是强正交可补的充分必要条件是,空间X是自反严格凸的. 相似文献
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Necessary and Sufficient Condition for Robust Stability and Stabilizability of Continuous-Time Linear Systems with Markovian Jumps 总被引:2,自引:0,他引:2
In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem. 相似文献
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In this paper we give a necessary and sufficient condition for the oscillation of the second order linear differential equation where p is a locally integrable function and either or where We give some applications which show how these results unify and imply some classical results in oscillation theory. 相似文献
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Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems 总被引:25,自引:0,他引:25
Liang Z. A. Huang H. X. Pardalos P. M. 《Journal of Optimization Theory and Applications》2001,110(3):611-619
In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions. 相似文献
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超线性奇异边值问题正解存在的充分必要条件 总被引:19,自引:1,他引:19
本文利用锥上的不动点定理给出了四阶超线性微分方程奇异边值问题C2[0,1]和C3[0,1]正解存在的充分必要条件. 相似文献
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本文研究带集合约束的向量极值问题。运用局部凸Hausdorff拓扑向量空间中广义次似凸映射的择一定理和其他一些结论,得到了关于集合约束向量极值问题弱有效解的几个充分必要条件. 相似文献