Exploiting Nonlinear Structures of Computational General Equilibrium Models: an Example with an Embedded Dantzig-Wolfe/Negishi Algorithm
by
Emmanuel Fragnière
University of Lausanne-HEC
Coauthors: Christian Condevaux-Lanloy (University of Geneva), Olivier Epelly (University of Geneva)

Economic models involving nonlinear programming techniques are often formulated in Algebraic Modeling Languages (AMLs) such as AMPL or GAMS since the syntax of writing a model in this environment closely resembles the mathematical notation when written on paper. One of the most important aspects of AMLs is their capability of dealing with nonlinear programs (NLP): a built-in interpretor evaluates nonlinear functions and their derivatives at points supplied by the nonlinear solver which only become known when the optimization proceeds. However, large-scale or complex nonlinear programming models may need customized solution techniques which cannot be easily hooked to AMLs. We believe that this difficulty can be circumvented by moving procedural statements contained in modeling languages into the algorithm. To this end, we developed a set of C++ routines, called SETNL, which can extract particular block structures and manipulate them in different ways along the solution process. This is performed via a flexible object-oriented approach which allows to implement a variety of solution techniques. The reference case is a demonstration version of MERGE, a dynamic general equilibrium model (GEM) developed by Manne and Richels. This GEM is formulated in GAMS as a welfare-optimization problem, following Negishi (see Rutherford). Negishi weights are unknown when solution starts and are iteratively determined. Without using SETNL, this is originally performed by a loop defined in the GAMS model itself. However, the use of SETNL first allows to implement this loop outside the modeling environment, second to exploit the special structure involved in the model optimized at each iteration.

Date received: January 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-08.