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
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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.Abstract:
Over the past decade, 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. This paper provides a state-of-the-art review of these developments as well as a summary of some open research topics in this growing field.read more
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Proximal Algorithms
Neal Parikh,Stephen Boyd +1 more
TL;DR: The many different interpretations of proximal operators and algorithms are discussed, their connections to many other topics in optimization and applied mathematics are described, some popular algorithms are surveyed, and a large number of examples of proxiesimal operators that commonly arise in practice are provided.
Book
Convex analysis and nonlinear optimization : theory and examples
TL;DR: In this paper, the Karush-Kuhn-Tucker Theorem and Fenchel duality were used for infinite versus finite dimensions, with a list of results and notation.
Journal ArticleDOI
Engineering and Economic Applications of Complementarity Problems
Michael C. Ferris,Jong-Shi Pang +1 more
TL;DR: The goal of this documentation is to summarize the essential applications of the nonlinear complementarity problem known to date, to provide a basis for the continued research on the non linear complementarityproblem, and to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Journal ArticleDOI
The path solver: a nommonotone stabilization scheme for mixed complementarity problems
TL;DR: The PATH solver as mentioned in this paper is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem, which employs a path generation procedure which is used to construct a piecewise-linear path from the current point to the Newton point; a step length acceptance criterion and a non-monotone path search are then used to choose the next iterate.
Journal ArticleDOI
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
TL;DR: It is shown that under appropriate assumptions on the latter mapping, any stationary point of the optimization problem is a global optimal solution, and hence solves the variational inequality problem.
References
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Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Journal ArticleDOI
Equilibrium points in n-person games
TL;DR: A concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple ofpure strategies, one strategy being taken for each player.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
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
Monotone Operators and the Proximal Point Algorithm
TL;DR: In this paper, the proximal point algorithm in exact form is investigated in a more general form where the requirement for exact minimization at each iteration is weakened, and the subdifferential $\partial f$ is replaced by an arbitrary maximal monotone operator T.