A Gauss-Seidel Type Solver for Special Convex Programs, with Application to Frictional Contact Mechanics

Abstract

An iterative method is described that solves the constrained minimisation of a convex function, when the constraints g j (x 1 ; ::; x n ) 0 are function of only a few variables and can be partitioned in some way. A proof of convergence is given which is based on the fact that the function values that are generated decrease. The relation to the non-linear equation solver TanGS [VKL93] is shown, together with some new results for TanGS. Finally the solver is applied to the solution of tangential traction in contact mechanics. Keywords convex optimalisation, Gauss-Seidel method, decomposition method, contact mechanics. 1 Introduction Convex programs (CP) arise naturally in contact mechanics as the discrete analogues of variational principles. They can be very large, when a fine discretisation is used. There can also be a large number of them, since the number of time steps can easily exceed 10.000 in the study of corrugation, and a few CP's must be solved per time step. It may thus be ..