An active set algorithm for a class of linear complementarity problems arising from rigid body dynamics

Abstract

An active set algorithm is introduced for positive definite and positive semi definite linear complementarity problems. The proposed algorithm is composed of two phases. Phase 1, the feasibility phase and phase 2, the optimality phase. In phase 1, the ellipsoid method is employed to test for feasibility and provide an advanced starting point if the problem is feasible. Providing such a warm start permits a good estimate of the active set. In phase 2, a criterion based on the complementarity condition is used to detect the working set per iteration until optimality is reached. This criterion leads to a valuable reduction in the size of the problem solved per iteration to obtain a search direction. Numerical examples are solved to illustrate the performance of the algorithm and a practical example in rigid body dynamics is solved to demonstrate the usage of the algorithm to solve such problems.

Unified primal-dual active set method for dynamic frictional contact problems

“…[23][24][25]). Recently proposed methods of semi-smooth Newton and primal-dual active (PDAS) type appear to be some of the most relevant methods for solving friction contact problems [26][27][28][29][30][31][32][33][34]. They are based on the following principle: the conditions of contact and friction are reformulated in terms of nonlinear complementarity functions whose solution is provided by the semismooth Newton method.…”

A primal-dual active set method for solving multi-rigid-body dynamic contact problems

“…Very few works have been devoted to this topic. We can cite, for instance, the work of Sharaf [29], in which a very particular class of rigid-body dynamics problems is considered, and the work of Koziara and Bicanic [30], for which a semismooth Newtonian method is proposed to solve problems dealing with pseudo-rigid bodies. Our goal in this work is to show the performance and efficiency of the primal-dual active set method for NSCD problems, compared with other effective methods based on the bipotential and augmented Lagrangian theories that have been recently developed [13].…”