A representation of the solution set of a class of linear complementarity problems. (1st February 2016)

• Record Type: Journal Article
• Authors: Phung, Huynh The
• Is Part Of: Optimization. Volume 65:Number 2(2016)
• Page Start: 289
• Page End: 298
• Publication Date: 2016-02-01
• Subjects: P-matrix -- P(−k)-matrix -- linear complementarity problem -- representation of solution set -- algorithm; Primary 90C33 -- Secondary 15A15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1022546
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Most of algorithms solving linear complementarity problems will terminate when a solution, or a proximate solution, is found or the problem is shown to have no solution. It is well known that if the underlying matrix belongs to the class, then the problem has a unique solution which could be found by various highly effective algorithms. However, when the matrix is not a -matrix the problem can have more than one solution, and these algorithms in general only find one of them. This article will produce a representation formula of the solution set of the linear complementarity problem with the underlying matrix belonging to a class much larger than . Based on the formula, an algorithm could be developed for completely solving the problem of this type.