Journal ArticleDOI
On the basic theorem of complementarity
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Using a fixed point theorem of Browder, the basic existence theorem of Lemke in linear complementarity theory is generalized to the nonlinear case.Abstract:
Using a fixed point theorem of Browder, the basic existence theorem of Lemke in linear complementarity theory is generalized to the nonlinear case.read more
Citations
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A Singular Value Thresholding Algorithm for Matrix Completion
TL;DR: This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.
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.
Book
Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
Journal ArticleDOI
A new inexact alternating directions method for monotone variational inequalities
TL;DR: The convergence of the proposed ADM method is proved under quite mild assumptions and flexible parameter conditions and the parameters to vary from iteration to iteration is proved.
Journal ArticleDOI
Homotopies for computation of fixed points
TL;DR: Given a point to set mapf on a simplex with certain conditions, an algorithm for computing fixed points is described, which operates by following the fixed point as an initially affine function is deformed towardsf.
References
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Journal ArticleDOI
Bimatrix Equilibrium Points and Mathematical Programming
TL;DR: In this paper, simple constructive proofs are given of solutions to the matric matric system Mz − ω = q; z ≧ 0; ω ≧ 1; zT = 0, for various kinds of data M, q, which embrace quadratic programming and the problem of finding equilibrium points of bimatrix games.
Journal ArticleDOI
On some non-linear elliptic differential-functional equations
TL;DR: In this paper, the results to be obtained can be considered as generalizations of some theorems of Gilbarg [5] and Stampacchia [14] in the case F [ u ] ~ 0.
Journal ArticleDOI
Complementary pivot theory of mathematical programming
TL;DR: The role of problems of the form w and z satisfying w = q + Mz, w = or 0, z = or0, zw = 0 play a fundamental role in mathematical programming.
Journal ArticleDOI
The Linear Complementarity Problem
TL;DR: In this article, it was shown that Lemke's algorithm will not solve the linear complementarity problem for a class of matrices, which properly includes copositive matrices with nonnegative principal minors, and matrices for bimatrix games.
Journal ArticleDOI
The complementarity problem
TL;DR: Several existence theorems are given under various conditions on the mapF, which cover the cases whenF is nonlinear nondifferentiable, nonlinear but differentiable, and affine.
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