共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
A relaxed projection method for variational inequalities 总被引:4,自引:0,他引:4
Masao Fukushima 《Mathematical Programming》1986,35(1):58-70
This paper presents a modification of the projection methods for solving variational inequality problems. Each iteration of the proposed algorithm consists of projection onto a halfspace containing the given closed convex set rather than the latter set itself. The algorithm can thus be implemented very easily and its global convergence to the solution can be established under suitable conditions.This work was supported in part by Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan. 相似文献
3.
In this note, by using some well-known results on properly efficient solutions of vector optimization problems, we show that the Pareto solution set of a vector variational inequality with a polyhedral constraint set can be expressed as the union of the solution sets of a family of (scalar) variational inequalities. 相似文献
4.
黄龙光 《应用泛函分析学报》2006,8(3):218-223
研究拓扑向量空间到其共轭空间的伪线性映射和其变分不等式问题,给出伪线性映射的几个等价形式,并对伪线性映射的变分不等式解集的特征进行了刻画. 相似文献
5.
本篇文章首先定义了向量变分不等式的严格可行点概念,其次在假设了映射是强(D)-伪单调的情况下,证明了向量变分不等式解集非空有界与其严格可行点存在的等价性问题,推广了在数量变分不等式上得到的相应结果. 相似文献
6.
Xiuyun Zheng 《Applied mathematics and computation》2010,216(12):3778-3785
In this paper, we propose a new projection method for the solution of variational inequality problems. The method is simple, which uses only function evaluations and projections onto the feasible set. We adopt a new step-size rule and a new search direction in the new method. Under the mild conditions, we prove the proposed method is globally convergent. Preliminary numerical results are reported. 相似文献
7.
In this paper, we study the local convergence behavior of four projection-type methods for the solution of the affine variational inequality (AVI) problem. It is shown that, if the sequence generated by one of the methods converges to a nondegenerate KKT point of the AVI problem, then after a finite number of iterations, some index sets in the dual variables at each iterative point coincide with the index set of the active constraints in the primal variables at the KKT point. As a consequence, we find that, after finitely many iterations, the four methods need not compute projections and their iterative equations are of reduced dimension. 相似文献
8.
本文在拓扩向量空间中研究一类Fuzzy映射的广义变分不等式问题,讨论了这类变分不等式解集的性质及满射性。本文结果改进、推广了作者在[1,2]中的相应结果。 相似文献
9.
Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities 总被引:3,自引:0,他引:3
Lu-Chuan Ceng Chang-yu Wang Jen-Chih Yao 《Mathematical Methods of Operations Research》2008,67(3):375-390
In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational
inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities
is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle
for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient
method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we
provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.
J.-C. Yao’s research was partially supported by a grant from the National Science Council. 相似文献
10.
A combined relaxation method for variational inequalities with nonlinear constraints 总被引:1,自引:0,他引:1
Igor V. Konnov 《Mathematical Programming》1998,80(2):239-252
A simple iterative method for solving variational inequalities with a set-valued, nonmonotone mapping and a convex feasible set is proposed. This set can be defined by nonlinear functions. The method is based on combining and extending ideas contained in various relaxation methods of nonsmooth optimization. Also a modification of the averaging method for the problem under consideration is proposed. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This research was supported in part by RFFI grant No. 95-01-00061. 相似文献
11.
D. R. Westbrook 《Journal of Computational and Applied Mathematics》1990,30(3):295-311
The numerical solution of the obstacle problem for beams and plates by means of variational inequalities and finite elements is examined. Algorithms for the solution of the discrete problem are discussed and particular attention is paid to different methods of approximating the constraint. The results of some numerical experiments for beams and plates are included. 相似文献
12.
AbstractWe propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem. 相似文献
13.
Junmin Chen Lijuan Zhang Tiegang Fan 《Journal of Mathematical Analysis and Applications》2007,334(2):1450-1461
Viscosity approximation methods for nonexpansive mappings are studied. Consider the iteration process {xn}, where x0∈C is arbitrary and xn+1=αnf(xn)+(1−αn)SPC(xn−λnAxn), f is a contraction on C, S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H. It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality. 相似文献
14.
In this paper, we first introduce the system of generalized implicit variational inequalities and prove the existence of its solution. Then we derive existence results for systems of generalized variational and variational like inequalities and system of variational inequalities. As applications, we establish some existence results for a solution to the system of optimization problems which includes the Nash equilibrium problem as a special case 相似文献
15.
《Optimization》2012,61(6):867-881
For the numerical solution of unilateral variational inequalities two iterative schemes are developed which provide approximations from below resp. from above. Both schemes are based on some kind of active set strategy and require the solution of an algebraic system of equations at each iteration step which is done by means of multigrid techniques. Convergence results are established and illustrated by some numerical results for the elastic-plastic torsion problem 相似文献
16.
《Optimization》2012,61(7):805-821
In this article we consider the problem of finding a common element in the solution set of generalized equilibrium problems, in the solution set of the classical variational inequality and in the fixed point set of strictly pseudocontractive mappings. Weak convergence theorems of common elements are established in real Hilbert spaces. 相似文献
17.
Xiaolin He 《Journal of Mathematical Analysis and Applications》2003,277(2):504-511
This paper shows that a continuous φ-strongly accretive mapping on a real Banach space is single-valued. And some recent results of set-valued variational inclusions and inequalities are discussed. 相似文献
18.
Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities 总被引:3,自引:0,他引:3
Bianchi M. Hadjisavvas N. Schaible S. 《Journal of Optimization Theory and Applications》2004,122(1):1-17
A coercivity condition is usually assumed in variational inequalities over noncompact domains to guarantee the existence of a solution. We derive minimal, i.e., necessary coercivity conditions for pseudomonotone and quasimonotone variational inequalities to have a nonempty, possibly unbounded solution set. Similarly, a minimal coercivity condition is derived for quasimonotone variational inequalities to have a nonempty, bounded solution set, thereby complementing recent studies for the pseudomonotone case. Finally, for quasimonotone complementarity problems, previous existence results involving so-called exceptional families of elements are strengthened by considerably weakening assumptions in the literature. 相似文献
19.
In this paper, we introduce a new three-step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution. We show that the sequence converges strongly to a common element of two sets under some control conditions. Results proved in this paper may be viewed as an improvement and refinement of the recent results of Noor and Huang [M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press] and Yao and Yao [Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press]. 相似文献
20.
We suggest and analyze some new splitting type projection methods for solving general variational inequalities by using the updating technique of the solution. The convergence analysis of these new methods is considered and the proof of convergence is very simple. These new methods are versatile. 相似文献