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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
01 Dec 2008
TL;DR: A new discrete velocity-level formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduces a simple fixed-point property of this coupled system allows a novel algorithm for accurate frictional Contact Resolution based on a simple staggered sequence of projections to be constructed.
Abstract: We present a new discrete velocity-level formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduce a simple fixed-point property of this coupled system This allows us to construct a novel algorithm for accurate frictional contact resolution based on a simple staggered sequence of projections The algorithm accelerates performance using warm starts to leverage the potentially high temporal coherence between contact states and provides users with direct control over frictional accuracy Applying this algorithm to rigid and deformable systems, we obtain robust and accurate simulations of frictional contact behavior not previously possible, at rates suitable for interactive haptic simulations, as well as large-scale animations By construction, the proposed algorithm guarantees exact, velocity-level contact constraint enforcement and obtains long-term stable and robust integration Examples are given to illustrate the performance, plausibility and accuracy of the obtained solutions

193 citations

Journal ArticleDOI
TL;DR: The cutting plane method relies on the service level functions being concave in the number of servers, and it is shown how to verify this requirement as the algorithm proceeds, and a numerical example showcases the properties of the method.
Abstract: We present an iterative cutting plane method for minimizing staffing costs in a service system subject to satisfying acceptable service level requirements over multiple time periods. We assume that the service level cannot be easily computed, and instead is evaluated using simulation. The simulation uses the method of common random numbers, so that the same sequence of random phenomena is observed when evaluating different staffing plans. In other words, we solve a sample average approximation problem. We establish convergence of the cutting plane method on a given sample average approximation. We also establish both convergence, and the rate of convergence, of the solutions to the sample average approximation to solutions of the original problem as the sample size increases. The cutting plane method relies on the service level functions being concave in the number of servers. We show how to verify this requirement as our algorithm proceeds. A numerical example showcases the properties of our method, and sheds light on when the concavity requirement can be expected to hold.

192 citations

Proceedings ArticleDOI
David Baraff1
01 Jul 1991
TL;DR: It is shown that computing contact forces according to this traditional principle is likely to require exponential time, and the principle for when impulses can occur is too restrictive, and a natural reformulation of the principle is proposed.
Abstract: Algorithms and computational complexity measures for simulating the motion of contacting bodies with friction are presented. The bodies are restricted to be perfectly rigid bodies that contact at finitely many points. Contact forces between bodies must satisfy the Coulomb model of friction. A traditional principle of mechanics is that contact forces are impulsive if and only if non-impulsive contact forces are insufficient to maintain the non-penetration constraints between bodies. When friction is allowed, it is known that impulsive contact forces can be necessary even in the absence of collisions between bodies. This paper shows that computing contact forces according to this traditional principle is likely to require exponential time. An analysis of this result reveals that the principle for when impulses can occur is too restrictive, and a natural reformulation of the principle is proposed. Using the reformulated principle, an algorithm with expected polynomial time behaviour for computing contact forces is presented.

191 citations


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

  • ...Iterative methods for quadratic programming and linear complementarity exist that can be adopted to this problem[14]....

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  • ...For non-PSD LCP’s with solutions, Lemke’s algorithm terminates either by finding a solution or by encountering an unbounded ray.1 As a result, Lemke’s algorithm is not suitable for solving non-PSD LCP’s....

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  • ...For frictionless systems, the LCP is always PSD and has a solution, so frictionless configurations do not have valid impulse solutions....

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  • ...The algorithm is exponential in the worst case, but has an expected running time polynomial in n[14]....

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  • ...However, for non-PSD LCP’s, Lemke’s algorithm is not guaranteed to terminate correctly (although it still takes only expected polynomial time to do so)....

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Journal ArticleDOI
TL;DR: It is shown that any stationary point of the unconstrained objective function is a solution of NCP if the mapping F involved in NCP is continuously differentiable and monotone, and that the level sets are bounded if F is continuous and strongly monotones.
Abstract: A reformulation of the nonlinear complementarity problem (NCP) as an unconstrained minimization problem is considered. It is shown that any stationary point of the unconstrained objective function is a solution of NCP if the mapping F involved in NCP is continuously differentiable and monotone, and that the level sets are bounded if F is continuous and strongly monotone. A descent algorithm is described which uses only function values of F. Some numerical results are given.

185 citations

Journal ArticleDOI
David Baraff1
TL;DR: Theoretical and practical issues in computing contact forces for systems with large numbers of contact points are considered and both systems of rigid bodies with and without Coulomb friction are studied.
Abstract: In rigid-body simulation it is necessary to compute the forces that arise between contacting bodies to prevent interpenetration. This paper studies the problem of rigid-body simulation when the bodies being simulated are restricted to contact at only finitely many points. Some theoretical and practical issues in computing contact forces for systems with large numbers of contact points are considered. Both systems of rigid bodies with and without Coulomb friction are studied. Complexity results are derived for certain classes of configurations and numerical methods for computing contact forces are discussed.

185 citations