Degree theory in linear complementarity

Abstract

In this paper, a brief survey of some of the results in linear complementarity theory is presented, using the conceptof the degree of a suitably constructed piecewise linear map. Local and global degrees of an LCP map are quiteuseful in identifying subclasses of and Qo-matrices. Some of the well-known characterizations of these classesare given a newer perspective in terms of degree theory. The class of superfluous matrices defined using globaldegree is highlighted with relevant examples. Properties of a simplicial polytope relating to an LCP map are of usein global degree analysis. One of the sections here deals with these results. Finally, the use of degree theory in thestudy of sensitivity and solution stability of linear complementarity problems is brought out.