NDLI: Dantzig—Wolfe Decomposition of Variational Inequalities

Content Provider	Springer Nature Link
Author	Fuller, J. David Chung, William
Copyright Year	2005
Abstract	The creation and ongoing management of a large economic model can be greatly simplified if the model is managed in separate smaller pieces defined, e.g. by region or commodity. For this purpose, we define an extension of Dantzig–Wolfe decomposition for the variational inequality (VI) problem, a modeling framework that is widely used for models of competitive or oligopolistic markets. The subproblem, a collection of independent smaller models, is a relaxed VI missing some “difficult” constraints. The subproblem is modified at each iteration by information passed from the last solution of the master problem in a manner analogous to Dantzig–Wolfe decomposition for optimization models. The master problem is a VI which forms convex combinations of proposals from the subproblem, and enforces the difficult constraints. A valid stopping condition is derived in which a scalar quantity, called the “convergence gap,” is monitored. The convergence gap is a generalization of the primal-dual gap that is commonly monitored in implementations of Dantzig–Wolfe decomposition for optimization models. Convergence is proved under conditions general enough to be applicable to many models. An illustration is provided for a two-region competitive model of Canadian energy markets.
Starting Page	303
Ending Page	326
Page Count	24
File Format	PDF
ISSN	09277099
Journal	Computational Economics
Volume Number	25
Issue Number	4
e-ISSN	15729974
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dantzig–Wolfe decomposition economic equilibrium variational inequality Economic Theory Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Economics, Econometrics and Finance Computer Science Applications

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