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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: In this article, a new modulus-based matrix splitting method was proposed to solve the linear complementarity problem, based on a new equivalent fixed-point form of the LCP.
Abstract: In this paper, to economically and fast solve the linear complementarity problem, based on a new equivalent fixed-point form of the linear complementarity problem, we establish a class of new modulus-based matrix splitting methods, which is different from the previously published works. Some sufficient conditions to guarantee the convergence of this new iteration method are presented. Numerical examples are offered to show the efficacy of this new iteration method. Moreover, the comparisons on numerical results show the computational efficiency of this new iteration method advantages over the corresponding modulus method, the modified modulus method and the modulus-based Gauss–Seidel method.
19 citations
TL;DR: This paper deals with the controllability of a class of nonsmooth complementarity mechanical systems, which are named juggling systems due to their particular structure and can be decomposed into an “object” and a “robot”.
19 citations
TL;DR: It is proved that convergence of the whole sequence generated by any of a large class of iterative algorithms for the symmetric linear complementarity problem (LCP), under the only hypothesis that a quadratic form associated with the LCP is bounded below on the nonnegative orthant.
Abstract: We prove convergence of the whole sequence generated by any of a large class of iterative algorithms for the symmetric linear complementarity problem (LCP), under the only hypothesis that a quadratic form associated with the LCP is bounded below on the nonnegative orthant. This hypothesis holds when the matrix is strictly copositive, and also when the matrix is copositive plus and the LCP is feasible. The proof is based upon the linear convergence rate of the sequence of functional values of the quadratic form. As a by-product, we obtain a decomposition result for copositive plus matrices. Finally, we prove that the distance from the generated sequence to the solution set (and the sequence itself, if its limit is a locally unique solution) have a linear rate of R-convergence.
19 citations
DOI•
01 Jan 2009
TL;DR: A new approach to contact force determination is presented, reformulate the contact force problem as a nonlinear root search problem, using a Fischer function, and solves this problem using a generalized Newton method.
Abstract: EUROGRAPHICS D L IGITAL IBRARY www.eg.org diglib.eg.org Abstract In interactive physical simulation, contact forces are applied to prevent rigid bodies from penetrating each other. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. The result is visual artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We reformulate the contact force problem as a nonlinear root search problem, using a Fischer function. We solve this problem using a generalized Newton method. Our new Fischer– Newton method shows improved qualities for specific configurations where the most widespread alternative, the Projected Gauss-Seidel method, fails. Experiments show superior convergence properties of the exact Fischer– Newton method.
19 citations
TL;DR: In this article, the projection-type error bound for the linear complementarity problem involving a matrix M and vector q is considered. And necessary and sufficient conditions on M and q for this error bound to hold globally, for all q such that the problem is solvable, are derived.
19 citations