Abstract. We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of the origi...

Based on a well-known reformulation of the linear complementarity problem (LCP) as a nondifferentiable system of nonlinear equations, a Newton-type method will be described for the solution of LCPs. Under certain assumptions, it will be shown that this method has a finite termination property, i.e., if an iterate is sufficiently close to a solution of LCP, the method finds this solution in one ...

We design a new continuation method for the solution of nonlinear complementarity problems with uniform P−functions. Similar to interior-point methods, we try to follow the central path inexactly. In contrast to interior-point methods, however, our iterates are allowed to stay outside of the positive orthant. The method is shown to be globally and superlinearly (quadratically) convergent.

In this paper, we present a family of smoothing methods to solve nonlinear complementarity problems (NCPs) involving P0-function. Several regularization or approximation techniques like Fisher-Burmeister’s method, interior-point (IPMs) approaches, already exist. All the corresponding sequence systems equations and depend on parameters that are difficult drive zero. The main novelty our approach...

In this paper we propose a power penalty approach to linear complementarity problems (LCP) in a finite dimensional space. This approach is based on approximating the LCP by a nonlinear equation with a power penalty term. We prove that the solution to this equation converges to that of the LCP at a rate equivalent to the reciprocal of the power used in the penalty term when the penalty parameter...

A new approach to model multiphase flow in porous media with phase appearance and disappearance is to use nonlinear complementarity constraints. In addition to the standard mass balance equations for mulitphase flow, a set of complementarity constraints are added in order to handle the phase transitions. This results in a larger system of nonlinear equations, which is non-smooth in general. The...

Interior point methods for nonlinear programs (NLP) are adapted for solution of mathematical programs with complementarity constraints (MPCCs). The constraints of the MPCC are suitably relaxed so as to guarantee a strictly feasible interior for the inequality constraints. The standard primal-dual algorithm has been adapted with a modified step calculation. The algorithm is shown to be superline...