Abstract :

In this talk, we shall look into the basics of the linear complementarity problem (LCP). Given a real square matrix $A$ of order $n$, LCP is the problem of determining if there is a nonnegative vector $x$ such that the vector $y=Ax=Q$ is nonnegative together with the complementarity condition $x^Ty=0$. The concepts of complementarity and linearity form a basis for the understanding of complex problems in mathematical and equilibrium programming and LCP assumes its significance from these. The connection of LCP to LPP shall also be discussed.