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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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Journal ArticleDOI
TL;DR: It is shown that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (LCP), and the proof results in three possible numerical solution methods for a given E LCP: regular ELCp algorithms, mixed integer linear programming algorithms, and regular LCP algorithms.

7 citations


Cites methods from "Linear complementarity, linear and ..."

  • ...For more information on the LCP and its applications we refer the interested reader to (Cottle et al., 1992; Ferris and Pang, 1997b; Ferris and Pang, 1997a; Leenaerts and van Bokhoven, 1998; Murty, 1988) and the references therein....

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01 Jun 1993
TL;DR: In this article, three different formulations are presented for expressing the initial motion direction of a system of contacting frictionless rigid bodies under gravity; the bodies are assumed to have no initial velocity.
Abstract: : Three different formulations are presented for expressing the initial motion direction of a system of contacting frictionless rigid bodies under gravity;. The bodies are assumed to have no initial velocity. The first formulation expresses the accelerations of the bodies in terms of the contact forces between the bodies. The contact forces are themselves expressed as the solution to a quadratic programming problem. The second formulation expresses the accelerations of the bodies according to Gauss' principle of least constraint. This principle is well-known to apply to systems with holonomic motion constraints (such as joints or hinges); in this paper, we show that the principle extends to the nonholonomic constraints that arise due to contact between bodies. The third formulation is conceptually the simplest; it says simply that the initial acceleration of the system is in the direction that most quickly decreases the gravitational potential energy of the system without violating the contact constraints between the bodies.

7 citations


Cites background from "Linear complementarity, linear and ..."

  • ...The first-order optimality conditions, or KKT conditions[10], for a constrained optimization problem are both necessary and sufficient when applied to a convex quadratic programming problem....

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Journal ArticleDOI
TL;DR: This new method provides a specific realization for the multisplitting method and generalizes many existing matrix splitting methods for linear complementarity problems and Convergence for this new method is proved when the coefficient matrix is an H"+-matrix.

7 citations

Book ChapterDOI
01 Jan 1997
TL;DR: This work focuses on usage models of Markov type and shows that by suitable changes of the probabilities of state transitions during test, the precision of the risk estimate can be optimized.
Abstract: A software usage models describes the prospective use of a program in its intended environment and allows the generation of random test cases leading to unbiased estimates of the failure risk, ie, the expected loss by program failure We concentrate on usage models of Markov type and show that by suitable changes of the probabilities of state transitions during test, the precision of the risk estimate can be optimized An algorithm for the computation of optimal transition probabilities is presented, and experimental results based on a C++ implementation of this algorithm are reported

7 citations


Cites methods from "Linear complementarity, linear and ..."

  • ...4 Numerical computation of the optimal transition probabilities For the numerical solution of (5), we use, in our implementation, an optimization algorithm of Frank{Wolfe{type (see [5], section 10....

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Journal ArticleDOI
TL;DR: In this article, a class of vertical implicit complementarity problems is introduced and necessary and sufficient conditions for the upper semi-continuity of the solution map to the vertical implicit homogeneous complementarity problem of type R0.
Abstract: In this paper, we introduce a class of vertical implicit complementarity problems and give a necessary and sufficient condition for the upper semi-continuity of the solution map to the vertical implicit homogeneous complementarity problem of type R0.

7 citations