共查询到20条相似文献,搜索用时 31 毫秒
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Satoru Takahashi 《Journal of Mathematical Analysis and Applications》2007,331(1):506-515
In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove a strong convergence theorem which is connected with Combettes and Hirstoaga's result [P.L. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 117-136] and Wittmann's result [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491]. Using this result, we obtain two corollaries which improve and extend their results. 相似文献
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A. Moudafi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):4083-4087
Based on the very recent work by Censor and Segal (2009) [1], and inspired by Xu (2006) [9], Zhao and Yang (2005) [10], and Bauschke and Combettes (2001) [2], we introduce and analyze an algorithm for solving the split common fixed-point problem for the wide class of quasi-nonexpansive operators in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related algorithms. 相似文献
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We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different viewpoint for the weak-to-strong principle of Bauschke and Combettes and unify many results concerning weak and strong convergence of subgradient type methods. 相似文献
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《Operations Research Letters》2022,50(1):40-44
We consider the numerical aspect of the multicommodity network equilibrium problem proposed by Rockafellar in 1995. Our method relies on the flexible monotone operator splitting framework recently proposed by Combettes and Eckstein. 相似文献
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Jonathan Eckstein 《Journal of Optimization Theory and Applications》2017,173(1):155-182
This paper develops what is essentially a simplified version of the block-iterative operator splitting method already proposed by the author and P. Combettes, but with more general initialization conditions. It then describes one way of implementing this algorithm asynchronously under a computational model inspired by modern high-performance computing environments, which consist of interconnected nodes each having multiple processor cores sharing a common local memory. The asynchronous implementation framework is then applied to derive an asynchronous algorithm which resembles the alternating direction method of multipliers with an arbitrary number of blocks of variables. Unlike earlier proposals for asynchronous variants of the alternating direction method of multipliers, the algorithm relies neither on probabilistic control nor on restrictive assumptions about the problem instance, instead making only standard convex-analytic regularity assumptions. It also allows the proximal parameters to range freely between arbitrary positive bounds, possibly varying with both iterations and subproblems. 相似文献
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Kazuhide Nakajo Kazuya Shimoji Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7025-7032
The hybrid method in mathematical programming was introduced by Haugazeau (1968) [1] and he proved a strong convergence theorem for finding a common element of finite nonempty closed convex subsets of a real Hilbert space. Later, Bauschke and Combettes (2001) [2] proposed some condition for a family of mappings (the so-called coherent condition) and established interesting results by the hybrid method. The authors (Nakajo et al., 2009) [10] extended Bauschke and Combettes’s results. In this paper, we introduce a condition weaker than the coherent condition and prove strong convergence theorems which generalize the results of Nakajo et al. (2009) [10]. And we get strong convergence theorems for a family of asymptotically κ-strict pseudo-contractions, a family of Lipschitz and pseudo-contractive mappings and a one-parameter uniformly Lipschitz semigroup of pseudo-contractive mappings. 相似文献
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The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of variational inequality for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend the recent results of Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515], Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43–52], Combettes and Hirstoaga [P.L. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 486–491], Iiduka and Takahashi, [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and many others. 相似文献
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目前的试验设计大体在连续空间或者无约束的离散空间下进行研究,但实际工程中不少场景都需要在离散空间中挑选试验点来进行试验设计,通常的试验设计方法无法应用于约束的离散空间中.文章立足于实际工程背景,基于连续空间下的均匀试验设计,采用Gale-Shapley算法,给出了连续空间到离散空间的映射设计方案.最后,结合实例进行了Gale-Shapley算法与经验方法所得设计的对比验证研究,在约束的离散空间下,Gale-Shapley算法所得到的映射设计具有更好的均匀性,且计算效率满足工程实际需求. 相似文献
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In this paper, we present a novel approach to design a code book for vector quantization using standard deviation. The proposed
algorithm optimizes the partitioning space to explore the search space for a set of equally viable and equivalent partitions.
Essentially the partition space is partitioned into perceptive clusters, so that the code book is optimized. The proposed
algorithm is proved better than the widely used quantization algorithm in applications. 相似文献
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《Optimization》2012,61(11):1895-1922
ABSTRACTIn this paper, we introduce a concept of A-sequences of Halpern type where A is an averaging infinite matrix. If A is the identity matrix, this notion become the well-know sequence generated by Halpern's iteration. A necessary and sufficient condition for the strong convergence of A-sequences of Halpern type is given whenever the matrix A satisfies some certain concentrating conditions. This class of matrices includes two interesting classes of matrices considered by Combettes and Pennanen [J. Math. Anal. Appl. 2002;275:521–536]. We deduce all the convergence theorems studied by Cianciaruso et al. [Optimization. 2016;65:1259–1275] and Muglia et al. [J. Nonlinear Convex Anal. 2016;17:2071–2082] from our result. Moreover, these results are established under the weaker assumptions. We also show that the same conclusion remains true under a new condition. 相似文献
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加罚Navier—Stokes方程的最佳非线性Galerkin算法 总被引:1,自引:0,他引:1
何银年 《数学物理学报(A辑)》1998,18(3):251-256
该文提出了求解二维加罚Navier-Stokes方程的最佳非线性Galerkin算法.这个算法在于在粗网格有限元空间上求解一非线性子问题,在细网格增量有限元空间Wh上求解一线性子问题.如果线性有限元被使用及,则该算法具有和有限元Galerkin算法同阶的收敛速度.然而该文提出的算法可以节省可观的计算时间. 相似文献
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Hiroshi Konno Yasutoshi Yajima Ayumi Ban 《Computational Optimization and Applications》1994,3(2):181-191
We will propose an algorithm for calculating a minimal sphere containing a polytope defined by a system of linear inequalities in low dimensional Euclidean space. This algorithm is a straightforward application of the algorithm for maximizing a convex quadratic function over a polytope. It will be shown that this algorithm successfully generates a minimal sphere when the dimensions of the underlying space is up to five.International Digital Communication Inc. 相似文献
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Harold P. Benson 《Journal of Global Optimization》2012,52(3):553-574
This article presents for the first time an algorithm specifically designed for globally minimizing a finite, convex function
over the weakly efficient set of a multiple objective nonlinear programming problem (V1) that has both nonlinear objective
functions and a convex, nonpolyhedral feasible region. The algorithm uses a branch and bound search in the outcome space of
problem (V1), rather than in the decision space of the problem, to find a global optimal solution. Since the dimension of
the outcome space is usually much smaller than the dimension of the decision space, often by one or more orders of magnitude,
this approach can be expected to considerably shorten the search. In addition, the algorithm can be easily modified to obtain
an approximate global optimal weakly efficient solution after a finite number of iterations. Furthermore, all of the subproblems
that the algorithm must solve can be easily solved, since they are all convex programming problems. The key, and sometimes
quite interesting, convergence properties of the algorithm are proven, and an example problem is solved. 相似文献
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针对目前混沌优化算法在选取局部搜索空间时的盲目性,提出一种具有自适应调节局部搜索空间能力的多点收缩混沌优化方法.该方法在当前搜索空间搜索时保留多个较好搜索点,之后利用这些点来确定之后的局部搜索空间,以达到对不同的函数和当前搜索空间内已进行搜索次数的自适应效果.给出了该算法以概率1收敛的证明.仿真结果表明该算法有效的提高了混沌优化算法的性能,改善了混沌算法的实用性. 相似文献
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Multiplicative programming problems (MPPs) are global optimization problems known to be NP-hard. In this paper, we employ algorithms developed to compute the entire set of nondominated points of multi-objective linear programmes (MOLPs) to solve linear MPPs. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solving one linear programme in each iteration, instead of two as the previous version indicates. We call this algorithm, which is based on Benson’s outer approximation algorithm for MOLPs, the primal objective space algorithm. Then, based on the dual variant of Benson’s algorithm, we propose a dual objective space algorithm for solving linear MPPs. The dual algorithm also requires solving only one linear programme in each iteration. We prove the correctness of the dual algorithm and use computational experiments comparing our algorithms to a recent global optimization algorithm for linear MPPs from the literature as well as two general global optimization solvers to demonstrate the superiority of the new algorithms in terms of computation time. Thus, we demonstrate that the use of multi-objective optimization techniques can be beneficial to solve difficult single objective global optimization problems. 相似文献
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本文提出一种基于均值的Toeplitz矩阵填充的子空间算法.通过在左奇异向量空间中对已知元素的最小二乘逼近,形成了新的可行矩阵;并利用对角线上的均值化使得迭代后的矩阵保持Toeplitz结构,从而减少了奇异向量空间的分解时间.理论上,证明了在一定条件下该算法收敛于一个低秩的Toeplitz矩阵.通过不同已知率的矩阵填充数值实验展示了Toeplitz矩阵填充的新算法比阈值增广Lagrange乘子算法在时间上和精度上更有效. 相似文献