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Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
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TL;DR: Numerical results indicate that ADMM is in general very efficient for solving symmetric EiCPs in terms of the number of iterations and computational effort, but is less efficient for the solution of nonsymmetric E iCPs.
Abstract: We introduce an Alternating Direction Method of Multipliers (ADMM) for finding a solution of the nonsymmetric Eigenvalue Complementarity Problem (EiCP). A simpler version of this method is proposed...
6 citations
Cites methods from "Linear complementarity, linear and ..."
...The so-called Murty’s least-index pivoting method [25] can be used for this purpose....
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DOI•
13 Nov 2008
TL;DR: This paper introduces a generic way of dealing with a set of different constraints (bilateral, unilateral, dry friction) in the context of interactive simulation and defines the notion of generalized constraints, which can be derived into most classical constraints types.
Abstract: This paper introduces a generic way of dealing with a set of different constraints (bilateral, unilateral, dry friction) in the context of interactive simulation. We show that all the mentioned constraints can be handled within a unified framework: we define the notion of generalized constraints, which can be derived into most classical constraints types. The solving method is based on an implicit treatment of constraints that provides good stability for interactive applications using deformable models and rigid bodies. Each constraint law is expressed in constraint subspace, making constraint evaluation much easier. A global solution is calculated using an iterative process that takes into account the mechanical coupling between the constraints. Various examples, from basic to more complex, show the practical advantage of using generalized constraints, as a way of creating heterogeneously constrained systems, as well as the scalability of the proposed method.
6 citations
Cites background from "Linear complementarity, linear and ..."
...In [Mur97], it is shown that the QP formulation can be equivalent to a linear complementarity problem (LCP) formulation....
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01 Sep 2015
TL;DR: A connection is established between users' centralities in their interdependence network, and their efforts at different interior equilibria of these games, which separate the effects of incoming and outgoing dependencies, as well as the influence of paths of different length, on users' effort levels.
Abstract: We consider the provision of non-excludable public goods on a network of interdependent strategic users. We study three different equilibria of these games, namely the Nash equilibrium, socially optimal, and exit equilibrium profiles. We identify properties of the interdependence graph that guarantee the existence and uniqueness of these equilibria. We further establish a connection between users' centralities in their interdependence network, and their efforts at different interior equilibria of these games. These characterizations separate the effects of incoming and outgoing dependencies, as well as the influence of paths of different length, on users' effort levels. We discuss some conceptual and practical implications of this centrality-effort connection.
6 citations
TL;DR: This paper proposes a new method using an alternating direction (AD) technique based on a modified symmetric successive overrelaxation (MSSOR) for LCP, assuming that the real matrix of the LCP is symmetric positive definite.
Abstract: Finding the solution of linear complementarity problem (LCP) is an important subject in scientific computing, engineering and economic applications In the literature, many iterative methods have been proposed, especially, when the matrix of the problem is a real positive definite or an H +? matrix In this paper, we propose a new method using an alternating direction (AD) technique based on a modified symmetric successive overrelaxation (MSSOR) for LCP, assuming that the real matrix of the LCP is symmetric positive definite This approach is an inner/outer iteration method, in which AD method is used as an outer iteration, and the MSSOR method as an inner one We provide a detailed proof for the convergence of the proposed method In addition, numerical results show that the proposed method is feasible and effective
6 citations
Cites background from "Linear complementarity, linear and ..."
...Well-known examples include the Nash equilibrium point of a bimatrix game, the contact problem, and the free boundary problem for journal bearings [19, 20, 29]....
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...Recently, modulus-based iterative methods have attracted much attention in the solution of LCP(q, A) [8, 17, 22, 25, 26, 29, 32, 36, 37]....
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TL;DR: In this paper, the three main versions discussed there use a ball of (a): 0 radius, (b): small positive radius, and (c): the largest possible radius with the given center that will completely fit within the polytope, with the option of changing its radius as the algorithm progresses.
Abstract: In [3, 1] gravitational methods for linear programming (LP) have been introduced. Several versions exist, the three main versions discussed there use a ball of (a): 0 radius, (b): small positive radius, and (c): the largest possible radius with the given center that will completely fit within the polytope, with the option of changing its radius as the algorithm progresses.
6 citations