A fixed point algorithm with economic applications

A new fixed point algorithm applicable to large scale economic problems is developed. Motivated by successive approximation the algorithm iterates on a convex combination of the traditional price to price map and the identity map. The actual combination used is determined from the convergence error...

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Bibliographic Details
Published in:Journal of economic dynamics & control 1985-10, Vol.9 (2), p.127-137
Main Authors: Khilnani, Arvind, Tse, Edison
Format: Article
Language:English
Subjects:
Algorithms
Applications
Approximation
Economic models
Economic theory
Mapping
Mathematical models
Supply & demand
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Summary:A new fixed point algorithm applicable to large scale economic problems is developed. Motivated by successive approximation the algorithm iterates on a convex combination of the traditional price to price map and the identity map. The actual combination used is determined from the convergence error of the previous iteration. The specified convex combination is guaranteed to be a contraction if the original map is Lipschitz continuous and antitonal. These sufficient conditions are shown to be weaker than the contraction requirement. A simple supply-demand example is presented to show the advantages of this algorithm over successive approximation.
ISSN:0165-1889
1879-1743
DOI:10.1016/0165-1889(85)90001-6