Iterative algorithms for the linear complementarity problem

Abstract

Direct complementary pivot algorithms for the linear complementarity problem with P-matrices are known to have exponential computational complexity. The analog of Gauss-Seidel and SOR iteration for linear complementarity problems with P-matrices has not been extensively developed. This paper extends some work of van Bokhoven to a class of nonsymmetric P-matrices, and develops and compares several new iterative algorithms for the linear complementarity problem. Numerical results for several hundred test problems are presented. Such indirect iterative algorithms may prove useful for large sparse complementarity problems.

Keywords:

• Linear complementarity problem
• P-matrix
• iterative algorithm
• fixed point iteration
• principal pivot submatrix
• contraction mapping
• computational complexity

C.R. Categories:

• G.1.3
• G.1.6
• G.4