Résumés
Abstract
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.
Keywords:
- linear complementarity problem,
- sufficient matrix,
- P-matrix,
- interior point method,
- affine scaling method,
- predictor-corrector algorithm
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