A representation of the solution set of a class of linear complementarity problems

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.

Keywords:

• P-matrix
• P^(−k)-matrix
• linear complementarity problem
• representation of solution set
• algorithm

AMS Subject Classifications:

• Primary 90C33
• Secondary 15A15

Acknowledgements

The author would like to thank the referees for their helpful comments and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research is funded by Vietnam NAFOSTED [grant number 101.02-2013.09].