ELA
DESCRIPTION OF ALL SOLUTIONS OF A LINEAR
COMPLEMENTARITY PROBLEM
∗JIRI ROHN†
Abstract. Description of all solutions of ann×nlinear complementarity problemx+=M x−+q
in terms of 2n
matrices and their Moore-Penrose inverses is given. The result is applied to describe all solutions of the absolute value equationAx+B|x|=b.
Key words. Linear complementarity problem, Moore-Penrose inverse, Verified solution, Abso-lute value equation.
AMS subject classifications.90C33.
∗Received by the editors February 5, 2009. Accepted for publication April 18, 2009. Handling
Editor: Raphael Loewy.
†Institute of Computer Science, Czech Academy of Sciences, Prague, and School of Business
Ad-ministration, Anglo-American University, Prague, Czech Republic (rohn@cs.cas.cz). Supported by the Czech Republic Grant Agency under grants 201/09/1957 and 201/08/J020, and by the Institu-tional Research Plan AV0Z10300504.
Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 246-252, April 2009
