### LANS Publications

# "Flexible Complementarity Solvers for Large-Scale Applications"

S. J. Benson and T. S. Munson

*Optimization Methods & Software*, vol. 21, no. 1, , pp. 155-168. Also Preprint ANL/MCS-P1055-0603

Preprint Version: [pdf]

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set methods that solve only one linear system of equations per iteration. The linear solver, preconditioner, and matrix structures can be chosen by the user for a particular application to achieve high parallel performance. The parallel scalability of these methods is demonstrated for some discretizations of infinite-dimensional variational inequalities.