In this chapter we give an overview of complementarity problems with a special focus on the extended linear complementarity problem (ELCP) and its applications in analysis and control of discrete-event systems such as traffic signal controlled intersections, manufacturing systems, railway networks, etc. We start by giving an introduction to the (regular) linear complementarity problem (LCP). Ne...

In this paper, we introduce a new class of generalized strongly set-valued nonlinear complementarity problems and construct new iterative algorithms. We show the existence of solutions for this kind of nonlinear complementarity problems and the convergence of iterative sequences generated by the algorithm. Our results extend some recent results in this field.

World trade in dairy products is being transformed by trade policy liberalization and technological change in dairy processing. The mixed complementarity problem formulation to modeling product-specific dairy trade can overcome a number of the limitations of existing optimization models, and can facilitate desirable extensions to previous analyses.

We introduce a new, one-parametric class of NCP-functions. This class subsumes the Fischer function and reduces to the minimum function in a limiting case of the parameter. This new class of NCP-functions is used in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. We present a detailed investigation of the properties of the equation operator, of the...

1993] proposed to solve nonlinear complementarity problems by seeking the unconstrained global minima of a new merit function which they called implicit Lagrangian. A crucial point in such an approach is to determine conditions which guarantee that every uncon-strained stationary point of the implicit Lagrangian is a global solution, since standard unconstrained minimization techniques are only...

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...

It has been shown by Lemke that if a matrix is copositive plus on IR n , then feasibility of the corresponding Linear Complementarity Problem implies solvability. In this article we show, under suitable conditions, that feasibility of a Generalized Linear Complementarity Problem (i.e., deened over a more general closed convex cone in a real Hilbert Space) implies solvability whenever the operat...

The linear complementarity problem (q,A) with data A ∈ Rn×n and q ∈ Rn involves finding a nonnegative z ∈ Rn such that Az+ q ≥ 0 and zt(Az+ q) = 0. Cottle and Stone introduced the class of P1-matrices and showed that if A is in P1\Q, then K(A) (the set of all q for which (q,A) has a solution) is a half-space and (q,A) has a unique solution for every q in the interior of K(A). Extending the resu...

A new smoothing algorithm for the solution of nonlinear complementarity problems (NCP) is introduced in this paper. It is based on semismooth equation reformulation of NCP by Fischer–Burmeister function and its related smooth approximation. In each iteration the corresponding linear system is solved only approximately. Since inexact directions are not necessarily descent, a nonmonotone techniqu...

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...