Efficient tridiagonal preconditioner for the matrix-free truncated Newton method

In this report, we study an efficient tridiagonal preconditioner, based on numerical differentiation, applied to the matrix-free truncated Newton method for unconstrained optimization. It is proved that this preconditioner is positive definite for many practical problems. The efficiency of the resulting matrix-free truncated Newton method is demonstrated by results of extensive numerical experiments. Citation Technical … Read more

Band preconditioners for the matrix-free truncated Newton method

This report is devoted to preconditioning techniques for the matrix-free truncated Newton method. After a review of basic known pproaches, we propose ew results concerning tridiagonal and pentadiagonal preconditioners based on the standard BFGS updates and on numerical differentiation. Furthermore, we present results of extensive numerical experiments serving for the careful comparison of suitable preconditioning … Read more

Computational experience with an interior point algorithm for large scale contact problems

In this paper we present an interior point method for large scale Signorini elastic contact problems. We study the case of an elastic body in frictionless contact with a rigid foundation. Primal and primal-dual algorithms are developed to solve the quadratic optimization problem arising in the variational formulation. Our computational study confirms the efficiency of … Read more