An active constraints Newton algorithm for the spatial price equilibrium problem

Abstract

We consider the general spatial price equilibrium problem. In order to solve such problems, we develop a Newton type algorithm that is combined with an active constraints strategy to handle the nonnegativety constraints or upper bounds on the variables. At each iteration of the algorithm, the choice of the initial active set is based on the value of the gradient and the dual variables. Two variants of the algorithm are presented: one in which the Newton equations are solved by the Gauss method and one in which these equations are solved by the conjugate gradient method. Computational results demonstrate the efficiency of the method.