Article ID: | iaor20105460 |
Volume: | 5 |
Issue: | 1 |
Start Page Number: | 1 |
End Page Number: | 12 |
Publication Date: | Jan 2010 |
Journal: | Algorithmic Operations Research |
Authors: | Terlaky Tamas, Nagy Marianna, Illes Tibor |
Keywords: | complementarity, interior point methods |
Linear Complementarity Problems (LCPs) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, our generalized interior point algorithms either solve the problems with rational coefficient matrix in polynomial time or give a polynomial size certificate that our matrix does not belong to the set of P * (˜κ) matrices, with arbitrary large, but apriori fixed, rational, positive ˜κ.