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A quadratically-convergent fixed-point algorithm for economic equilibria and linearly constrained optimization

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Abstract

Fixed-point algorithms for computing equilibria in economies with production or stationary points in constrained optimization generally use point-to-set mappings and therefore converge slowly. An alternative implementation uses continuous functions with a higher dimensionality corresponding to the inclusion of activity levels or dual variables. Here we develop algorithms that only increase the dimensionality implicitly. The solution path is piecewise-linear as in other algorithms. However, when viewed in the low-dimensional space, the path within each simplex can be piecewise-linear rather than linear. Asymptotically, these paths are linear and quadratic convergence is attained.

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Authors and Affiliations

  1. Cornell University, Ithaca, NY, USA

    Michael J. Todd

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  1. Michael J. Todd
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Additional information

This research was partially supported by NSF Grant ENG76-08749.

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Todd, M.J. A quadratically-convergent fixed-point algorithm for economic equilibria and linearly constrained optimization. Mathematical Programming 18, 111–126 (1980). https://doi.org/10.1007/BF01588307

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  • DOI: https://doi.org/10.1007/BF01588307

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