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On Dynamic MultiRigidBody Contact Problems with Coulomb Friction
"... . This paper is summary of a comprehensive study of the problem of predicting the possible acceleration(s) of a set of rigid, threedimensional bodies in contact in the presence of Coulomb friction. We begin with a brief introduction to this problem and a survey of related work and previous approach ..."
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Cited by 90 (18 self)
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. This paper is summary of a comprehensive study of the problem of predicting the possible acceleration(s) of a set of rigid, threedimensional bodies in contact in the presence of Coulomb friction. We begin with a brief introduction to this problem and a survey of related work and previous approaches. This is followed by the introduction of two novel complementarity formulations for the contact problem under two friction laws: Coulomb's Law and an analogous law in which Coulomb's quadratic friction cone is approximated by a pyramid. Under a full column rank assumption on the system Jacobian matrix, we establish the existence and uniqueness of a solution to our new models in the case where the friction coefficients are nonnegative and sufficiently small. For the model based on the friction pyramid law, we also show that the classical Lemke almostcomplementary pivot algorithm and our new feasible interior point method are guaranteed to compute a solution. Extensive computational result...
On a Homogeneous Algorithm for the Monotone Complementarity Problem
 Mathematical Programming
, 1995
"... We present a generalization of a homogeneous selfdual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any "bigM" parameter or twophase method, and it generates either a solution converging towards feasibility an ..."
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Cited by 38 (3 self)
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We present a generalization of a homogeneous selfdual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any "bigM" parameter or twophase method, and it generates either a solution converging towards feasibility and complementarity simultaneously or a certificate proving infeasibility. Moreover, if the MCP is polynomially solvable with an interior feasible starting point, then it can be polynomially solved without using or knowing such information at all. To our knowledge, this is the first interiorpoint and infeasiblestarting algorithm for solving the MCP that possesses these desired features. Preliminary computational results are presented. Key words: Monotone complementarity problem, homogeneous and selfdual, infeasiblestarting algorithm. Running head: A homogeneous algorithm for MCP. Department of Management, Odense University, Campusvej 55, DK5230 Odense M, Denmark, email: eda@busieco.ou.dk. y De...