Several papers have appeared recently establishing the analyticity of the central path at the boundary point for both linear programming (LP) and linear complementarity problems (LCP). While the proofs for LP are long, proceeding from limiting properties of the corresponding derivatives, the proofs for LCP are very simple, consisting of an application of the implicit function theorem to a certa...

The extended linear complementarity problem and linear complementary-slackness systems * B. De Schutter If you want to cite this report, please use the following reference instead: B. De Schutter, " The extended linear complementarity problem and linear complementary-slackness systems, "

In this article, we introduce the class of semimonotone star ($E_0^s$) matrices. We establish importance $E_0^s$-matrices in context complementarity theory. show that principal pivot transform $E_0^s$-matrix is not necessarily $E_0^s$ general. However, prove $\tilde{E_0^s}$-matrices, a subclass with some additional conditions, $E_0^f$ by showing $P_0.$ LCP$(q, A)$ can be processable Lemke's alg...

We revisit the class of column competent matrices and study some matrix theoretic properties this class. The local w-uniqueness solutions to linear complementarity problem can be identified by matrices. establish new results on in connection with These are significant context theory as well algorithms operations research. prove locally property Finally, we a between adequate help degree theory.

For getting the numerical solution of linear complementary problem (LCP), there are many methods such as modulus-based matrix splitting iteration and nonsmooth Newton?s method. We proposed Square-Newton method to solve LCP. This could LCP efficiently. gave theoretical analysis experiments in paper.