A Decomposition Approach for a Class of Economic Equilibrium Models

In this paper we present the theoretical foundations for one of the methods used to achieve convergence in the National Energy Modeling System (NEMS). NEMS is a large model with several component models that are built and operated by different branches in the organization and is an example of a system without a hierarchical structure that cannot be solved by traditional equation solving methods. Some of the component models use linear programs to construct supply and demand curves. The discontinuities that result lead to oscillations in the standard relaxation algorithms. We explain where the convergence problems lie and how the convergence theory with step functions links to the convergence theory with continuous functions. To achieve convergence within the entire system, a set of ad hoc techniques were developed to implement a decomposition strategy that allows the individual models to be run separately. We present the theoretical justification for one of them here. The technique presented here has the potential to allow an organization to use operational models for planning without resorting to aggregation. It also facilitates decentralized computing over Internet.