共查询到20条相似文献,搜索用时 31 毫秒
1.
在无穷维Hillbert空间中研究了一类单调型变分不等式,把求单调型变分不等式解的问题转化为求强单调变分不等式的解,建立了一种新的迭代算法,并证明了由算法生成的迭代序列强收敛于单调变分不等式的解,从而推广了所列文献中的许多重要结果. 相似文献
2.
Hideaki Iiduka 《Journal of Optimization Theory and Applications》2011,148(3):580-592
Many practical problems such as signal processing and network resource allocation are formulated as the monotone variational
inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms to solve these problems have been
proposed. This paper discusses a monotone variational inequality with variational inequality constraint over the fixed point
set of a nonexpansive mapping, which is called the triple-hierarchical constrained optimization problem, and presents an iterative
algorithm for solving it. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain
assumptions. 相似文献
3.
In this paper, a new notion of Knaster–Kuratowski–Mazurkiewicz mapping is introduced and a generalized Knaster–Kuratowski–Mazurkiewicz
theorem is proved. As applications, some existence theorems of solutions for (vector) Ky Fan minimax inequality, Ky Fan section
theorem, variational relation problems, n-person noncooperative game, and n-person noncooperative multiobjective game are obtained. 相似文献
4.
E. G. Gol’shtein 《Computational Mathematics and Mathematical Physics》2011,51(9):1483-1488
An equilibrium problem is studied whose special case is finding a Nash point in a noncooperative multiperson game. A numerical
algorithm for solving this problem is described. Conditions on the problem are stated under which an estimate is obtained
for the convergence rate of the algorithm to a unique solution of the problem. The results are used for a numerical analysis
of noncooperative games. 相似文献
5.
I. V. Konnov 《Set-Valued and Variational Analysis》2016,24(3):499-516
We consider an extension of a noncooperative game problem where players have joint binding constraints. We suggest a shares allocation approach, which replaces the initial problem with a sequence of Nash equilibrium problems together with an upper level set-valued variational inequality as master problem. This transformation maintains the monotonicity properties of the underlying mappings. We also show that the regularization yields a decomposable penalty method, which removes complex functions in constraints within the custom noncooperative game framework and provides the single-valued master problem with strengthened monotonicity of its cost mapping. 相似文献
6.
7.
Numerical Algorithms - In this paper, we propose Linesearch methods for solving a bilevel split variational inequality problem (BSVIP) involving a strongly monotone mapping in the upper-level... 相似文献
8.
This paper is concerned with the existence of an optimal control problem for a quasi-linear elliptic obstacle variational inequality in which the obstacle is taken as the control. Firstly, we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in Section 2. In Section 3, as an application, without the assumption of the monotone type mapping for the leading operator of the variational inequality, we prove that the leading operator of the variational inequality is a monotone type mapping. Existence of the optimal obstacle is proved. The method used here is different from [Y.Y. Zhou, X.Q. Yang, K.L. Teo, The existence results for optimal control problems governed by a variational inequality, J. Math. Anal. Appl. 321 (2006) 595-608]. 相似文献
9.
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
10.
1.引言 变分不等式问题在数学规划中起着重要作用,它最初作为研究偏微分方程的工具,首先由 Fishera和 Stampacchia等于六十年代初提出,可参看[1]及其参考文献,之后也被广泛用于研究经济学和运筹学等领域中的均衡模型,互补问题和凸规划问题都是变分不等式问题的特殊情形,文献[2]对有限维变分不等式问题和非线性互补问题的理论、算法及应用作了十分全面的综述.设 C是实有限维空间 Rn,的非空闲凸子集, F是 Rn → Rn的映射,本文讨论的变分不等式问题VI(C,F)是: 求向量r*∈C.使得:F(… 相似文献
11.
Nguyen Buong Pham Thi Thu Hoai Nguyen Duong Nguyen 《Journal of Fixed Point Theory and Applications》2017,19(4):2383-2395
In this paper, we introduce implicit and explicit iterative methods for solving a variational inequality problem over the set of zeros for a maximal monotone mapping in Hilbert spaces. As consequence, new modifications of the proximal point method are obtained. 相似文献
12.
Min Zhang Deren Han Gang Qian Xihong Yan 《Journal of Optimization Theory and Applications》2012,152(3):675-695
We propose a new decomposition method for solving a class of monotone variational inequalities with linear constraints. The
proposed method needs only to solve a well-conditioned system of nonlinear equations, which is much easier than a variational
inequality, the subproblem in the classic alternating direction methods. To make the method more flexible and practical, we
solve the sub-problems approximately. We adopt a self-adaptive rule to adjust the parameter, which can improve the numerical
performance of the algorithm. Under mild conditions, the underlying mapping be monotone and the solution set of the problem
be nonempty, we prove the global convergence of the proposed algorithm. Finally, we report some preliminary computational
results, which demonstrate the promising performance of the new algorithm. 相似文献
13.
Changjie Fang Ying Wang Shaokang Yang 《Journal of Fixed Point Theory and Applications》2016,18(1):27-43
In this paper, we suggest two new iterative methods for finding a common element of the solution set of a variational inequality problem and the set of fixed points of a contraction mapping in Hilbert space. We also present weak and strong convergence theorems for these new methods, provided that the fixed point mapping is a θ-strict pseudocontraction and the mapping associated with the variational inequality problem is monotone. The results presented in this paper improve and unify important recent results announced by many authors. 相似文献
14.
We make use of the Banach contraction mapping principle to prove the linear convergence of a regularization algorithm for
strongly monotone Ky Fan inequalities that satisfy a Lipschitz-type condition recently introduced by Mastroeni. We then modify
the proposed algorithm to obtain a line search-free algorithm which does not require the Lipschitz-type condition. We apply
the proposed algorithms to implement inexact proximal methods for solving monotone (not necessarily strongly monotone) Ky
Fan inequalities. Applications to variational inequality and complementarity problems are discussed. As a consequence, a linearly
convergent derivative-free algorithm without line search for strongly monotone nonlinear complementarity problem is obtained.
Application to a Nash-Cournot equilibrium model is discussed and some preliminary computational results are reported. 相似文献
15.
In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive mapping and solutions of variational inequality problem for monotone mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive mappings and solutions set of finite family of variational inequality problems for continuous monotone mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings. 相似文献
16.
Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak convergence result. In this paper, we use viscosity approximation methods and some related knowledge to solve a class of generalized SFP’s with monotone variational inequalities in Hilbert space. We propose some iterative algorithms based on viscosity approximation methods and get strong convergence theorems. As applications, we can use algorithms we proposed for solving split variational inequality problems (SVIP), split constrained convex minimization problems and some related problems in Hilbert space. 相似文献
17.
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link in the relationship between the solution sets to these various regularized problems is the idea of exact regularization, which, in turn, is fundamentally associated with the existence of Lagrange multipliers for the regularized variational inequality. A regularization is said to be exact if a solution to the regularized problem is a solution to the unregularized problem for all parameters beyond a certain value. The Lagrange multipliers corresponding to a particular regularization of a variational inequality, on the other hand, are defined via the dual gap function. Our analysis suggests various conceptual, iteratively regularized numerical schemes, for which we provide error bounds, and hence stopping criteria, under the additional assumption that the solution set to the unregularized problem is what we call weakly sharp of order greater than one. 相似文献
18.
《Optimization》2012,61(9):1841-1854
We introduce a new iteration method for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of strict pseudocontractions in a real Hilbert space. The weak convergence of the iterative sequences generated by the method is obtained thanks to improve and extend some recent results under the assumptions that the cost mapping associated with the variational inequality problem only is pseudomonotone and not necessarily inverse strongly monotone. Finally, we present some numerical examples to illustrate the behaviour of the proposed algorithm. 相似文献
19.
20.
D. Han 《Applied Mathematics and Optimization》2002,45(1):63-74
The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever
the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as
structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating
direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just
makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results
to illustrate the efficiency of the method.
Accepted 4 May 2001. Online publication 19 October, 2001. 相似文献