Interior point algorithms for general LCPs

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∗(κ̃) matrices, with arbitrary large, but apriori fixed, rational, positive κ̃. Key words: linear complementarity problem, sufficient matrix, P∗-matrix, interior point method, affine scaling method, predictor-corrector algorithm