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Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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

Illes, T. and Nagy, M. and Terlaky, T. (2010) A polynomial path-following interior point algorithm for general linear complementarity problems. Journal of Global Optimization, 47 (3). pp. 329-342. ISSN 0925-5001

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Abstract

Linear Complementarity Problems (LCPs) belong to the class of -complete problems. Therefore we cannot expect a polynomial time solution method for LCPs 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.