In this paper, an interior-point algorithm  for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...

The paper discusses three general classes of nonlinear programming models. Our objective is to show how to represent optimization problem, such as nonlinear programs, in a compact format using extended mathematical programming. This is a useful tool, especially in cases when complementarity representation, such as mixed complementarity problems, could be difficult to apply. We reflect on the sp...

In this paper we deene the Extended Linear Complementarity Problem (ELCP), an extension of the well-known Linear Complementarity Problem (LCP). We study the general solution set of an ELCP and we present an algorithm to nd all its solutions. Finally we show that the ELCP can be used to solve some important problems in the max algebra.

In this paper, the solution of the symmetric Quadratic Eigenvalue Complementarity Problem (QEiCP) is addressed. The QEiCP has a solution provided the so-called co-regular and co-hyperbolic properties hold and is said to be symmetric if all the matrices involved in its definition are symmetric. We show that under the two conditions stated above the symmetric QEiCP can be reduced to the problem o...

We introduce a family of parallel Newton-Krylov-Schwarz methods for solving complementarity problems. The methods are based on a smoothed grid sequencing method, a semismooth inexact Newton method, and a twogrid restricted overlapping Schwarz preconditioner. We show numerically that such an approach is highly scalable in the sense that the number of Newton iterations and the number of linear it...

In this paper we deene 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 nd all its solutions. We also show that the general ELCP is an N...

Given f: Rn+ ~ R n, the complementarity problem is to find a solution to x > O, f(x) >_ 0, and (x, f(x)) = 0. Under the condition that fis continuously differentiable, we prove that for a generic set of such an f, the problem has a discrete solution set. Also, under a set of generic non-degeneracy conditions and a condition that implies existence, we prove that the problem has an odd number of ...

In this paper, we discuss the Eigenvalue Complementarity Problem (EiCP) where at least one of its defining matrices is asymmetric. A sufficient condition for the existence of a solution to the EiCP is established. The EiCP is shown to be equivalent to finding a global minimum of an appropriate merit function on a convex set Ω defined by linear constraints. A sufficient condition for a stationar...

A Mathematical Program with Linear Complementarity Constraints (MPLCC) is an optimization problem where a continuously differentiable function is minimized on a set defined by linear constraints and complementarity conditions on pairs of complementary variables. This problem finds many applications in several areas of science, engineering and economics and is also an important tool for the solu...

This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each pla...