Mathematica Eterna
Open Access

Abstract

An improved ODE-type filter method with smooth approximation function

Mingxi Lu and Ke Su

In this paper, we propose an improved ODE-type filter method. Compared to other methods, at each iteration, only one linear system needs to be solved in our algorithm . Also , this method is more flexible and less computational scale. By using the Fischer-Burmeister function, we reformulate complementarity problems to a system of nonlinear and nonsmooth equations. Furthermore, we use the Kanzow function to approximate the Fischer-Burmeister function so that smooth and nonlinear equations can be obtained. Under some reasonable conditions, the global convergence results of our algorithm is presented.