TY - JOUR AU - Illés, Tibor AU - Nagy, Marianna AU - Terlaky, Tamás PY - 2010/04/14 Y2 - 2024/03/29 TI - Polynomial Interior Point Algorithms for General Linear Complementarity Problems JF - Algorithmic Operations Research JA - AOR VL - 5 IS - 1 SE - Articles DO - UR - https://journals.lib.unb.ca/index.php/AOR/article/view/11067 SP - Pages 1 - 12 AB - 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. ER -