Incomplete Decomposition Algorithms for Discrete Dynamic Nonlinear Models

The problem of solving block triangular nonlinear systems of equations appears in several applications in industrial, social and environmental contexts. Those systems are given by (F 1 (x 1 ); F 2 (x 1 ; x 2 ); : : : ; Fm (x 1 ; x 2 ; : : : ; xm )) = 0: The most usual way of solving such systems consists on solving sequentially the different n i \Theta n i partial systems, F i (x 1 ; \Delta \Delta \Delta ; x i ) = 0. Some Newtonian approaches, where the system is considered as a whole and solved by Newton, quasi-Newton or inexact Newton methods have also been considered in the literature. In this paper it is proposed a "team model" scheme in which the system is also considered as a whole. Each iteration is constructed in m steps and for solving the partial problem F i (x 1 ; \Delta \Delta \Delta ; x i ) = 0 one is free to use any appropriate iterative method. A convergence theorem is proved and the algorithm is used to solve a dynamic model based on complementarity. Keywords. Nonlinea..