In this paper we define the Extended Linear Complementarity Problem (ELCP), an extension of the well-known Linear Complementarity Problem (LCP). We show that the ELCP can be viewed as a kind of unifying framework for the LCP and its various generalizations. We study the general solution set of an ELCP and we develop an algorithm to find all its solutions. We also show that the general ELCP is a...

In this paper we consider the European continuous installment call option. Then  its linear complementarity formulation is given. Writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. Finally finite element method is applied to price the European continuous installment call option.

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

In this paper we consider some extensions of the Linear Complementarity Problem, which is one of the fundamental problems in mathematical programming. More specifically we consider the Linear Dynamic Complementarity Problem (LDCP), the Generalized Linear Complementarity Problem (GLCP) and the Extended Linear Complementarity Problem (ELCP). We show that the LDCP is a special case of the ELCP and...

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...