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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.

Item type: Article
ID code: 14418
Keywords: linear complementarity problems, LCPs, polynomial, sufficient matrix, long-step method, Management. Industrial Management, Control and Optimization, Management Science and Operations Research, Applied Mathematics, Computer Science Applications
Subjects: Social Sciences > Industries. Land use. Labor > Management. Industrial Management
Department: Strathclyde Business School > Management Science
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Depositing user: Mrs Caroline Sisi
Date Deposited: 27 Jan 2010 14:42
Last modified: 18 Apr 2014 05:00
URI: http://strathprints.strath.ac.uk/id/eprint/14418

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