Journal ArticleDOI
A relaxed projection method for variational inequalities
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Each iteration of the proposed algorithm consists of projection onto a halfspace containing the given closed convex set rather than the latter set itself, so its global convergence to the solution can be established under suitable conditions.Abstract:
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.read more
Citations
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Journal ArticleDOI
Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications
Patrick T. Harker,Jong-Shi Pang +1 more
TL;DR: The field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory as mentioned in this paper.
Journal ArticleDOI
The relaxed CQ algorithm solving the split feasibility problem
TL;DR: In this article, a modified version of the CQ algorithm, called the relaxed CQ, is given, in which we replace PC and PQ by and, respectively, and the latter is easy to implement.
Journal ArticleDOI
A note on the CQ algorithm for the split feasibility problem
Biao Qu,Biao Qu,Naihua Xiu +2 more
TL;DR: Yang et al. as discussed by the authors proposed a modified version of the CQ algorithm by adopting Armijo-like searches and showed convergence of the modified algorithm under mild conditions, where the objective function does not require matrix inverses and the largest eigenvalue of the matrix ATA.
Journal ArticleDOI
Solving the split feasibility problem without prior knowledge of matrix norms
TL;DR: In this paper, the authors introduce a way of selecting the stepsizes such that the implementation of the CQ algorithm does not need any prior information about the operator norm, which is the most popular iterative method for the split feasibility problem.
References
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Book
An introduction to variational inequalities and their applications
TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
Journal ArticleDOI
Traffic Equilibrium and Variational Inequalities
TL;DR: This work uses the techniques of the theory of variational inequalities to establish existence of a traffic equilibrium pattern, to design an algorithm for the construction of this pattern and to derive estimates on the speed of convergence of the algorithm.
Book ChapterDOI
Some continuity properties of polyhedral multifunctions
TL;DR: A multifunction is polyhedral if its graph is the union of finitely many polyhedral convex sets as discussed by the authors, and it is shown how these properties can be applied to such areas as linear complementarity and parametric programming.
Journal ArticleDOI
Regularity and Stability for Convex Multivalued Functions
TL;DR: Multivalued functions with convex graphs are shown to exhibit certain desirable regularity properties when their ranges have internal points to develop a perturbation theory for convex inequalities and to extend results on the continuity of convex functions.
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