共查询到19条相似文献,搜索用时 93 毫秒
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非线性最优化一个超线收敛的可行下降算法 总被引:7,自引:0,他引:7
本文讨论非线性等式和不等式约束最优化的求解方法。首先将原问题扩充成一个只含不等式约束的参数规划,对于充分大的参数,扩充问题与原问题是等价的。然手建立具有以下特点的一个新算法。1)算法对扩充问题而言是可行下降的,参数只须自动调整有限次;2)每次迭代仅需解一个二次规划;3)在适当的假设下,算法超线性收敛于原问题的最优解。 相似文献
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荣祯 《应用泛函分析学报》2012,14(1):109-112
给出了求解单调变分不等式的两类迭代算法.通过解强单调变分不等式子问题,产生两个迭代点列,都弱收敛到变分不等式的解.最后,给出了这两类新算法的收敛性分析. 相似文献
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2020年Liu和Yang提出了求解Hilbert空间中拟单调且Lipschitz连续的变分不等式问题的投影算法,简称LYA。本文在欧氏空间中提出了一种新的求解拟单调变分不等式的压缩投影算法,简称NPCA。新算法削弱了LYA中映射的Lipschitz连续性。在映射连续、拟单调且对偶变分不等式解集非空的条件下得到了NPCA所生成点列的聚点是解的结论。当变分不等式的解集还满足一定条件时,得到了NPCA的全局收敛性。数值实验结果表明NPCA所需的迭代步数少于LYA的迭代步数,NPCA在高维拟单调例子中所需的计算机耗时也更少。 相似文献
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非线性约束最优化一族超线性收敛的可行方法 总被引:5,自引:0,他引:5
本文建立求解非线性不等式约束最优化一族含参数的可行方法.算法每次迭代仅需解一个规模较小的二次规划.在一定的假设条件下,证明了算法族的全局收敛性和超线性收敛性. 相似文献
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讨论变分不等式问题VIP(X,F),其中F是单调函数,约束集X为有界区域.利用摄动技术和一类光滑互补函数将问题等价转化为序列合两个参数的非线性方程组,然后据此建立VIP(X,F)的一个内点连续算法.分析和论证了方程组解的存在性和惟一性等重要性质,证明了算法很好的整体收敛性,最后对算法进行了初步的数值试验。 相似文献
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非线性不等式约束最优化一个超线性与二次收敛的强次可行方法 总被引:1,自引:0,他引:1
本文讨论非线性不等式约束最优化问题,借助于序列线性方程组技术和强次可行方法思想,建立了问题的一个初始点任意的快速收敛新算法.在每次迭代中,算法只需解一个结构简单的线性方程组.算法的初始迭代点不仅可以是任意的,而且不使用罚函数和罚参数,在迭代过程中,迭代点列的可行性单调不减.在相对弱的假设下,算法具有较好的收敛性和收敛速度,即具有整体与强收敛性,超线性与二次收敛性.文中最后给出一些数值试验结果. 相似文献
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本文改进了[3]中的一个基本不等式和原算法,从而提高了数值计算的效率,而且在新算法的收敛性分析中去掉了变分不等式问题的单调性条件. 相似文献
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In this paper, we consider a system of general variational inclusions in q-uniformly smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for the system of general variational inclusions. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature. 相似文献
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Solution differentiability for variational inequalities 总被引:1,自引:0,他引:1
Jerzy Kyparisis 《Mathematical Programming》1990,48(1-3):285-301
In this paper we study solution differentiability properties for variational inequalities. We characterize Fréchet differentiability of perturbed solutions to parametric variational inequality problems defined on polyhedral sets. Our result extends the recent result of Pang and it directly specializes to nonlinear complementarity problems, variational inequality problems defined on perturbed sets and to nonlinear programming problems. 相似文献
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P. Tossings 《Applied Mathematics and Optimization》1994,29(2):125-159
Following the works of R. T. Rockafellar, to search for a zero of a maximal monotone operator, and of B. Lemaire, to solve convex optimization problems, we present a perturbed version of the proximal point algorithm. We apply this new algorithm to convex optimization and to variational inclusions or, more particularly, to variational inequalities. 相似文献
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§1. IntroductionSiddiqiandAnsari[4]developediterativealgorithmsforfindingapproximatesolutiontonewclassesofquasivariationalinequalitiesinHilbertspaces,HassouniandMoudafi[1]extendthemainideasofpaper[4]tomoregeneralcases,whichconsideredaclassofvariation… 相似文献
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Jerzy Kyparisis 《Annals of Operations Research》1990,27(1):143-173
This paper surveys the main results in the area of sensitivity analysis for finite-dimensional variational inequality and nonlinear complementarity problems. It provides an overview of Lipschitz continuity and differentiability properties of perturbed solutions for variational inequality problems, defined on both fixed and perturbed sets, and for nonlinear complementarity problems. 相似文献
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Xi LiNan-jing Huang 《Applied mathematics and computation》2011,217(22):9053-9061
In this paper, a concept of graph convergence concerned with the H(·, ·)-accretive operator is introduced in Banach spaces and some equivalence theorems between of graph-convergence and resolvent operator convergence for the H(·, ·)-accretive operator sequence are proved. As an application, a perturbed algorithm for solving a class of variational inclusions involving the H(·, ·)-accretive operator is constructed. Under some suitable conditions, the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the perturbed algorithm are also given. 相似文献
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This study is intended to provide a modified variational algorithm for the numerical solution of a class of self‐adjoint singularly perturbed boundary value problem, which is equally applicable to other classes of problems. The principle of the method lies in the introduction of a mixed piecewise domain decomposition and manipulating the variational iterative approach for tackling this class of problems. The uniform convergence of the technique to the exact solution is demonstrated. Numerical results, computational comparisons, suitable error measures and illustrations are provided to testify efficiently and demonstrate the convergence, efficiency and applicability of the method. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Chih-Sheng Chuang 《Optimization》2016,65(4):811-825
In this paper, we study the well-posedness for the parametric optimization problems with variational inclusion problems as constraint (or the perturbed problem of optimization problems with constraint). Furthermore, we consider the relation between the well-posedness for the parametric optimization problems with variational inclusion problems as constraint and the well-posedness in the generalized sense for variational inclusion problems. 相似文献