Journal ArticleDOI
A Class of Projection and Contraction Methods for Monotone Variational-Inequalities
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TLDR
In this article, a new class of iterative methods for solving monotone variational inequalities is introduced, where each iteration consists essentially only of the computation ofF(u), a projection to Ω,v:=P ≥ 0, and the mappingF(v) The distance of the iterates to the solution set monotonically converges to zero.Abstract:
In this paper we introduce a new class of iterative methods for solving the monotone variational inequalities
$$u* \in \Omega , (u - u*)^T F(u*) \geqslant 0, \forall u \in \Omega $$
Each iteration of the methods presented consists essentially only of the computation ofF(u), a projection to Ω,v:=P
Ω[u-F(u)], and the mappingF(v) The distance of the iterates to the solution set monotonically converges to zero Both the methods and the convergence proof are quite simpleread more
Citations
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Journal ArticleDOI
Some developments in general variational inequalities
TL;DR: This paper presents a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection, Wiener-Hopf equations, updating the solution, auxiliary principle, inertial proximal, penalty function, dynamical system and well-posedness.
Journal ArticleDOI
Parallel Multi-Block ADMM with o(1 / k) Convergence
TL;DR: The classic ADMM can be extended to the N-block Jacobi fashion and preserve convergence in the following two cases: (i) matrices A_i and Ai are mutually near-orthogonal and have full column-rank, or (ii) proximal terms are added to theN subproblems (but without any assumption on matrices $$A_i$$Ai).
Journal ArticleDOI
Improvements of some projection methods for monotone nonlinear variational inequalities
Bingsheng He,Li-Zhi Liao +1 more
TL;DR: In this article, the relationship of projection-type methods for monotone nonlinear variational inequalities was investigated and improvements were made. But the work in this paper is restricted to the case where the proximal point method is the corresponding implicit method.
Journal ArticleDOI
Inertial projection and contraction algorithms for variational inequalities
TL;DR: A modified version of the algorithm to find a common element of the set of solutions of a variational inequality and theset of fixed points of a nonexpansive mapping in H.
Journal ArticleDOI
Projection methods, algorithms, and a new system of nonlinear variational inequalities
TL;DR: In this paper, the convergence of projection methods is based on a new iterative algorithm for the approximation-solvability of the following system of nonlinear variational inequalities (SNVI): determine elements x*, y* ϵ K such that 〈ϱT(y*) + x* − y*, x − x*
References
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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.
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On the basic theorem of complementarity
TL;DR: Using a fixed point theorem of Browder, the basic existence theorem of Lemke in linear complementarity theory is generalized to the nonlinear case.
Journal ArticleDOI
Iterative methods for variational and complementarity problems
Jong-Shi Pang,D. Chan +1 more
TL;DR: This paper studies both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems and several convergence results are obtained for some nonlinear approximation methods.
Journal ArticleDOI
An iterative scheme for variational inequalities
TL;DR: A general iterative scheme for the numerical solution of finite dimensional variational inequalities that contains the projection, linear approximation and relaxation methods but also induces new algorithms and allows the possibility of adjusting the norm at each step of the algorithm.
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