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, "

The mixed complementarity problem can be reformulated as a nonsmooth equation by using the median operator. In this paper, we rst study some useful properties of this reformulation and then derive the Chen-Harker-Kanzow-Smale smoothing function for the mixed complementarity problem. On the basis of this smoothing function, we present a smoothing Newton method for solving the mixed complementari...

In e-learning environments, tutors perform the main function of tutoring. They follow up learners and answer their assistance requests which require different skills. These requests may not belong to the tutors’ skills and competencies, so collaboration among other tutors is expected. In fact, this collaboration can improve tutors’ skills and provide learners with effective monitoring. It can b...

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.