In this paper we establish the existence of a discrete zero point of a function from the n-dimensional integer lattice Z to the n-dimensional Euclidean space IR under very general conditions with respect to the behaviour of the function. The proof is constructive and uses a combinatorial argument based on a simplicial algorithm with vector labeling and lexicographic linear programming pivot ste...

We consider the Fold Complementarity Problem, which is one of the recent subjects in complementarity theory. It is a mathematical model used in economics in the study of distributive problems (cf. [25], [5]). A particular case is the k-Fold Complementarity Problem, studied using a variant of the notion of Z-function by A. Villar [25]. In this way, Villar obtained the solution of this problem as...

We present a new approach to solving nonlinear complementarity problems based on the normal map and adaptations of the projected gradient algorithm. We characterize a Gauss{Newton point for nonlinear complementarity problems and show that it is suucient to check at most two cells of the related normal manifold to determine such points. Our algorithm uses the projected gradient method on one cel...

Non-linear complementarity problems (NCPs) are often solved by iterative methods based on a generalization of the classical Newton method and its modifications for smooth equations. We consider a method with modification of the right-hand side vector for a reformulation of the semi-smooth equation arising from the NCP and prove local convergence of the proposed method. Some numerical results ar...

A natural damping of Newton's method for nonsmooth equations is presented. This damping, via the path search instead of the traditional line search, enlarges the domain of convergence of Newton's method and therefore is said to be globally convergent. Convergence behavior is like that of line search damped Newton's method for smooth equations, including Q-quadratic convergence rates under appro...

A novel inexact smoothing method is presented for solving the second-order cone complementarity problems (SOCCP). Our method reformulates the SOCCP as an equivalent nonlinear system of equations by introducing a regularized Chen-Harker-Kanzow-Smale smoothing function. At each iteration, Newton’s method is adopted to solve the system of equations approximately, which saves computation work compa...

Abstract. In competitive electric reserve markets, the suppliers face the optimal allocation problem of their reserve capacities in order to purse their profit maximizing. Under this background, we develop a capacity allocation model as nonlinear programming. Nonlinear complementarity method is utilized to search for the optimal solution. And smoothing technique is applied to get a system of sm...

We study the problem of solving a constrained system of nonlinear equations by a combination of the classical damped Newton method for (unconstrained) smooth equations and the recent interior point potential reduction methods for linear programs, linear and nonlin-ear complementarity problems. In general, constrained equations provide a uniied formulation for many mathematical programming probl...

We present a new algorithm for the solution of general (not necessarily monotone) complementarity problems. The algorithm is based on a reformulation of the complementarity problem as a nonsmooth system of equations by using the Fischer-Burmeister function. We use an idea by Chen, Qi and Sun and apply a Jacobian smoothing method (which is a mixture between nonsmooth Newton and smoothing methods...