Linear complementarity problem (LCP) is studied. After reforming general LCP as the system of nonlinear equations by NCP-function, equivalent to solving an unconstrained optimization model, which can be solved a recently proposed algorithm named novel global harmony search (NGHS). NGHS overcome disadvantage interior-point methods. Numerical results show that has higher rate convergence than oth...

T paper shows how many types of combinatorial problems can be embedded in continuous space and solved as nonconvex optimization problems. If the objective function and the constraints are linear, problems of this kind can be formulated as linear complementarity problems. An algorithm is presented to solve this type of problem and indicate its convergence properties. Computational comparisons ar...

A simple and uniied analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P-linear complementarity problem (P-LCP). It is shown that the rate of local convergence of a-order algorithm with a centering step is + 1 if there is a strictly complementary solution and (+ 1)=2 otherwise. For the-order algorithm without the centerin...

Piecewise linear (PL) modelling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modelling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks. In this paper the object of study will be dynamic electrical circuits that can be recast as li...

We present an overview of our research on the use of generalized linear complementarity problems (LCPs) for analysis of continuously variable systems and discrete event systems. We indicate how the Generalized LCP can be used to analyze piecewise-linear resistive electrical circuits. Next we discuss how the Extended LCP can be used to solve some fundamental problems that arise in max-algebraic ...

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, 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...