International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 2, Pages 99-113
doi:10.1155/S0161171202007056
Projective algorithms for solving complementarity problems
1Department of Mathematics, State University of New York at Geneseo, Geneseo 14454, NY, USA
2Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy 12180, NY, USA
Received 16 February 2001
Copyright © 2002 Caroline N. Haddad and George J. Habetler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We present robust projective algorithms of the von Neumann type
for the linear complementarity problem and for the generalized
linear complementarity problem. The methods, an extension of
Projections Onto Convex Sets (POCS) are applied to a class of
problems consisting of finding the intersection of closed
nonconvex sets. We give conditions under which convergence occurs
(always in 2 dimensions, and in practice, in higher dimensions)
when the matrices are P-matrices (though not necessarily
symmetric or positive definite). We provide numerical results
with comparisons to Projective Successive Over
Relaxation (PSOR).