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This paper presents a fast first-order method for solving the quasi-staticcontact problem with the Coulomb friction. It is known that this problem can beformulated as a second-order cone linear complementarity problem, for whichregularized or semi-smooth Newton methods are widely used. As an alternativeapproach, this paper develops a method based on an accelerated primal-dualalgorithm. The proposed method is easy to implement, as most of computationconsists of additions and multiplications of vectors and matrices. Numericalexperiments demonstrate that this method outperforms a regularized and smoothedNewton method for the second-order cone complementarity problem.

Primal-dual algorithm for quasi-static contact problem with Coulomb's friction