Parallel and Serial Variational Inequality Decomposition Algorithms for Multicommodity Market Equilibrium Problems

Abstract

We have applied parallel and serial variational inequality (VI) diagonal decomposition algorithms to large-scale, multicommodity market equilibrium problems. These decomposition algorithms resolve the VI problems into single commodity problems, which are then solved as quadratic programming problems. The algorithms are implemented on an IBM 3090-600E, and randomly gen erated linear and nonlinear problems with as many as 100 markets and 12 commodities are solved. The com putational results demonstrate that the parallel diagonal decomposition scheme is amenable to paralielization. This is the first time that multicommodity equilibrium problems of this scale and level of generality have been solved. Furthermore, this is the first study to compare the efficiencies of parallel and serial VI decomposition algorithms. Although we have selected as a prototype an equilibrium problem in economics, virtually any equilibrium problem can be formulated and studied as a variational inequality problem. Hence, our results are not limited to applications in economics and operations research.