A polynomial path-following interior point algorithm for general linear complementarity problems

• Published in: Journal of global optimization Vol. 47; no. 3; pp. 329 - 342
• Main Authors: Illés, Tibor, Nagy, Marianna, Terlaky, Tamás
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.07.2010; Springer Nature B.V
• Subjects: Algorithms; Computer Science; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Real Functions; Science; Interior point method; Linear complementarity problem; matrix; Sufficient matrix; Long-step method
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-008-9348-0

Linear Complementarity Problems ( LCP s) belong to the class of -complete problems. Therefore we cannot expect a polynomial time solution method for LCP s without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of the original problem or detects the lack of property , with arbitrary large, but apriori fixed ). In the latter case, the algorithms give a polynomial size certificate depending on parameter , the initial interior point and the input size of the LCP ). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following interior point algorithms.