共查询到20条相似文献,搜索用时 78 毫秒
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求解变分不等式问题.通过构造一个新的光滑逼近函数,建立了解变分不等式问题的一个非内点连续算法.在一定条件下证明了该算法的全局收敛性和局部二次收敛性.数值实验表明该算法对求解变分不等式问题是可行有效的. 相似文献
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交替方向法是求解可分离结构变分不等式问题的经典方法之一, 它将一个大型的变分不等式问题分解成若干个小规模的变分不等式问题进行迭代求解. 但每步迭代过程中求解的子问题仍然摆脱不了求解变分不等式子问题的瓶颈. 从数值计算上来说, 求解一个变分不等式并不是一件容易的事情.因此, 本文提出一种新的交替方向法, 每步迭代只需要求解一个变分不等式子问题和一个强单调的非线性方程组子问题. 相对变分不等式问题而言, 我们更容易、且有更多的有效算法求解一个非线性方程组问题. 在与经典的交替方向法相同的假设条件下, 我们证明了新算法的全局收敛性. 进一步的数值试验也验证了新算法的有效性. 相似文献
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1997 年, 交通网络分析方面的问题把我引进乘子交替方向法(ADMM)的研究领域. 近10 年来, 原本用来求解变分不等式的ADMM在优化计算中被广泛采用, 影响越来越大. 这里总结了20 年来我们在ADMM 方面的工作, 特别是近10 年 ADMM 在凸优化分裂收缩算法方面的进展. 梳理主要结果, 说清来龙去脉. 文章利用变分不等式的形式研究凸优化的ADMM 类算法, 论及的所有方法都能纳入一个简单的预测-校正统一框架. 在统一框架下证明算法的收缩性质特别简单. 通读, 有利于了解ADMM类算法的概貌. 仔细阅读, 也许就掌握了根据实际问题需要构造分裂算法的基本技巧. 也要清醒地看到, ADMM类算法源自增广拉格朗日乘子法 (ALM) 和邻近点 (PPA)算法, 它只是便于利用问题的可分离结构, 并没有消除 ALM和PPA等一阶算法固有的缺点. 相似文献
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考虑和分析了一类求解广义集值变分不等式的一类新的外梯度算法,该方法包含几个新的和已知的算法作为特例.改进了求解变分不等式及其相关的优化问题的已有的许多结果. 相似文献
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广义混合似变分不等式组的两步迭代算法 总被引:1,自引:0,他引:1
对H ilbert空间中一类广义混合似变分不等式组进行了研究;利用次微分算子的预解式技术,建立了广义混合似变分不等式组与不动点问题之间的等价关系;给出了一个求解这种广义混合似变分不等式组的显式两步迭代算法;并证明了该算法在适当的条件下收敛. 相似文献
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拟变分不等式问题在经济、工程,最优化和控制等领域都有着广泛的应用,目前,对拟变分不等式问题的研究还处于初级阶段.在本文中,我们利用梯度投影技术,给出了一种求解拟变分不等式问题的投影类算法,证明了该算法的全局收敛性,并给出了数值试验结果. 相似文献
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G. Woo S. Kim R. V. Namm S. A. Sachkoff 《Computational Mathematics and Mathematical Physics》2006,46(11):1932-1939
An algorithm for seeking a saddle point for the semicoercive variational Signorini inequality is studied. The algorithm is based on an iterative proximal regularization of a modified Lagrangian functional. 相似文献
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In this paper, we first characterize finite convergence of an arbitrary iterative algorithm for solving the variational inequality problem (VIP), where the finite convergence means that the algorithm can find an exact solution of the problem in a finite number of iterations. By using this result, we obtain that the well-known proximal point algorithm possesses finite convergence if the solution set of VIP is weakly sharp. As an extension, we show finite convergence of the inertial proximal method for solving the general variational inequality problem under the condition of weak g-sharpness. 相似文献
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We propose an iterative algorithm for solving a semicoercive nonsmooth variational inequality. The algorithm is based on the stepwise partial smoothing of the minimized functional and an iterative proximal regularization method.We obtain a solution to the variational Mosolov and Myasnikov problem with boundary friction as a limit point of a sequence of solutions to stable auxiliary problems. 相似文献
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Godwin Chidi Ugwunnadi Abdul Rahim Khan Mujahid Abbas 《Journal of Fixed Point Theory and Applications》2018,20(2):82
We introduce a hybrid proximal point algorithm and establish its strong convergence to a common solution of a proximal point of a lower semi-continuous mapping and a fixed point of a demicontractive mapping in the framework of a CAT(0) space. As applications of our new result, we solve variational inequality problems for these mappings on a Hilbert space. Illustrative example is given to validate theoretical result obtained herein. 相似文献
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In this paper, we establish sufficient conditions for guaranteeing finite termination of an arbitrary algorithm for solving a variational inequality problem in a Banach space. Applying these conditions, it shows that sequences generated by the proximal point algorithm terminate at solutions in a finite number of iterations. 相似文献
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L. C. Ceng B. S. Mordukhovich J. C. Yao 《Journal of Optimization Theory and Applications》2010,146(2):267-303
This paper studies a general vector optimization problem of finding weakly efficient points for mappings from Hilbert spaces
to arbitrary Banach spaces, where the latter are partially ordered by some closed, convex, and pointed cones with nonempty
interiors. To find solutions of this vector optimization problem, we introduce an auxiliary variational inequality problem
for a monotone and Lipschitz continuous mapping. The approximate proximal method in vector optimization is extended to develop
a hybrid approximate proximal method for the general vector optimization problem under consideration by combining an extragradient
method to find a solution of the variational inequality problem and an approximate proximal point method for finding a root
of a maximal monotone operator. In this hybrid approximate proximal method, the subproblems consist of finding approximate
solutions to the variational inequality problem for monotone and Lipschitz continuous mapping, and then finding weakly efficient
points for a suitable regularization of the original mapping. We present both absolute and relative versions of our hybrid
algorithm in which the subproblems are solved only approximately. The weak convergence of the generated sequence to a weak
efficient point is established under quite mild assumptions. In addition, we develop some extensions of our hybrid algorithms
for vector optimization by using Bregman-type functions. 相似文献
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Boris S. Mordukhovich Barbara Panicucci Massimo Pappalardo Mauro Passacantando 《Optimization Letters》2012,6(7):1535-1550
This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions. 相似文献
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In this paper, we investigate the proximal point algorithm (in short PPA) for variational inequalities with pseudomonotone vector fields on Hadamard manifolds. Under weaker assumptions than monotonicity, we show that the sequence generated by PPA is well defined and prove that the sequence converges to a solution of variational inequality, whenever it exists. The results presented in this paper generalize and improve some corresponding known results given in literatures. 相似文献
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Error bounds for proximal point subproblems and associated inexact proximal point algorithms 总被引:1,自引:0,他引:1
We study various error measures for approximate solution of proximal point regularizations of the variational inequality problem,
and of the closely related problem of finding a zero of a maximal monotone operator. A new merit function is proposed for
proximal point subproblems associated with the latter. This merit function is based on Burachik-Iusem-Svaiter’s concept of
ε-enlargement of a maximal monotone operator. For variational inequalities, we establish a precise relationship between the
regularized gap function, which is a natural error measure in this context, and our new merit function. Some error bounds
are derived using both merit functions for the corresponding formulations of the proximal subproblem. We further use the regularized
gap function to devise a new inexact proximal point algorithm for solving monotone variational inequalities. This inexact
proximal point method preserves all the desirable global and local convergence properties of the classical exact/inexact method,
while providing a constructive error tolerance criterion, suitable for further practical applications. The use of other tolerance
rules is also discussed.
Received: April 28, 1999 / Accepted: March 24, 2000?Published online July 20, 2000 相似文献
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In this paper, we introduce the notion of a weak sharp set of solutions to a variational inequality problem (VIP) in a reflexive, strictly convex and smooth Banach space, and present its several equivalent conditions. We also prove, under some continuity and monotonicity assumptions, that if any sequence generated by an algorithm for solving (VIP) converges to a weak sharp solution, then we can obtain solutions for (VIP) by solving a finite number of convex optimization subproblems with linear objective. Moreover, in order to characterize finite convergence of an iterative algorithm, we introduce the notion of a weak subsharp set of solutions to a variational inequality problem (VIP), which is more general than that of weak sharp solutions in Hilbert spaces. We establish a sufficient and necessary condition for the finite convergence of an algorithm for solving (VIP) which satisfies that the sequence generated by which converges to a weak subsharp solution of (VIP), and show that the proximal point algorithm satisfies this condition. As a consequence, we prove that the proximal point algorithm possesses finite convergence whenever the sequence generated by which converges to a weak subsharp solution of (VIP). 相似文献