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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   

3.
《Optimization》2012,61(5):1239-1261
We provide two weakly convergent algorithms for finding a zero of the sum of a maximally monotone operator, a cocoercive operator, and the normal cone to a closed vector subspace of a real Hilbert space. The methods exploit the intrinsic structure of the problem by activating explicitly the cocoercive operator in the first step, and taking advantage of a vector space decomposition in the second step. The second step of the first method is a Douglas–Rachford iteration involving the maximally monotone operator and the normal cone. In the second method, it is a proximal step involving the partial inverse of the maximally monotone operator with respect to the vector subspace. Connections between the proposed methods and other methods in the literature are provided. Applications to monotone inclusions with finitely many maximally monotone operators and optimization problems are examined.  相似文献   

4.
Phung M. Duc 《Optimization》2016,65(10):1855-1866
We propose splitting, parallel algorithms for solving strongly equilibrium problems over the intersection of a finite number of closed convex sets given as the fixed-point sets of nonexpansive mappings in real Hilbert spaces. The algorithm is a combination between the gradient method and the Mann-Krasnosel’skii iterative scheme, where the projection can be computed onto each set separately rather than onto their intersection. Strong convergence is proved. Some special cases involving bilevel equilibrium problems with inverse strongly monotone variational inequality, monotone equilibrium constraints and maximal monotone inclusions are discussed. An illustrative example involving a system of integral equations is presented.  相似文献   

5.
This article deals with numerical solutions of a general class of coupled nonlinear elliptic equations. Using the method of upper and lower solutions, monotone sequences are constructed for difference schemes which approximate coupled systems of nonlinear elliptic equations. This monotone convergence leads to existence‐uniqueness theorems for solutions to problems with reaction functions of quasi‐monotone nondecreasing, quasi‐monotone nonincreasing and mixed quasi‐monotone types. A monotone domain decomposition algorithm which combines the monotone approach and an iterative domain decomposition method based on the Schwarz alternating, is proposed. An application to a reaction‐diffusion model in chemical engineering is given. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 621–640, 2012  相似文献   

6.
《Optimization》2012,61(11):2099-2124
ABSTRACT

In this paper, we propose new subgradient extragradient methods for finding a solution of a strongly monotone equilibrium problem over the solution set of another monotone equilibrium problem which usually is called monotone bilevel equilibrium problem in Hilbert spaces. The first proposed algorithm is based on the subgradient extragradient method presented by Censor et al. [Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335]. The strong convergence of the algorithm is established under monotone assumptions of the cost bifunctions with Lipschitz-type continuous conditions recently presented by Mastroeni in the auxiliary problem principle. We also present a modification of the algorithm for solving an equilibrium problem, where the constraint domain is the common solution set of another equilibrium problem and a fixed point problem. Several fundamental experiments are provided to illustrate the numerical behaviour of the algorithms and to compare with others.  相似文献   

7.
一些类型的数学规划问题的全局最优解   总被引:4,自引:0,他引:4  
本文对严格单调函数给出了几个凸化和凹化的方法,利用这些方法可将一个严格单调的规划问题转化为一个等价的标准D.C.规划或凹极小问题.本文还对只有一个严格单调的约束的非单调规划问题给出了目标函数的一个凸化和凹化方法,利用这些方法可将只有一个严格单调约束的非单调规划问题转化为一个等价的凹极小问题.再利用已有的关于D.C.规划和凹极小的算法,可以求得原问题的全局最优解.  相似文献   

8.
Computational formulae for scalar derivatives of mappings and pairs of mappings in the direction of a set will be given. These formulae are very important for explicitly verifying conditions of existence for fixed point theorems, surjectivity theorems, integral equations, variational inequalities and complementarity problems under additional differentiability conditions. To emphasize this idea at the end of the paper we give an application to complementarity problems. Some theorems which extend the correspondence between monotone mappings and scalar derivatives from Euclidean spaces to Hilbert spaces will also be given.  相似文献   

9.
Inspired by the success of the projected Barzilai-Borwein (PBB) method for large-scale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods, it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.  相似文献   

10.
The aim of this article is to present several computational algorithms for numerical solutions of a nonlinear finite difference system that represents a finite difference approximation of a class of fourth‐order elliptic boundary value problems. The numerical algorithms are based on the method of upper and lower solutions and its associated monotone iterations. Three linear monotone iterative schemes are given, and each iterative scheme yields two sequences, which converge monotonically from above and below, respectively, to a maximal solution and a minimal solution of the finite difference system. This monotone convergence property leads to upper and lower bounds of the solution in each iteration as well as an existence‐comparison theorem for the finite difference system. Sufficient conditions for the uniqueness of the solution and some techniques for the construction of upper and lower solutions are obtained, and numerical results for a two‐point boundary‐value problem with known analytical solution are given. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:347–368, 2001  相似文献   

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