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Simplicial zero-point algorithms: A unifying description

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Abstract

In this paper, we consider the limiting paths of simplicial algorithms for finding a zero point. By rewriting the zero-point problem as a problem of finding a stationary point, the problem can be solved by generating a path of stationary points of the function restricted to an expanding convex, compact set. The limiting path of a simplicial algorithm to find a zero point is obtained by choosing this set in an appropriate way. Almost all simplicial algorithms fit in this framework. Using this framework, it can be shown very easily that Merrill's condition is sufficient for convergence of the algorithms.

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Author information

Authors and Affiliations

  1. Department of Actuarial Sciences and Econometrics, Free University, Amsterdam, The Netherlands

    G. van der Laan (Associate Professor)

  2. Department of Econometrics, Tilburg University, Tilburg, The Netherlands

    A. J. J. Talman (Associate Professor)

Authors
  1. G. van der Laan
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  2. A. J. J. Talman
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Additional information

Communicated by O. L. Mangasarian

This research is part of the VWF project “Disequilibrium and Equilibrium in Demand and Supply,” which has been approved by the Dutch Office of Education and Sciences. The authors are grateful to the referees for helpful comments which have improved the presentation of the paper.

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van der Laan, G., Talman, A.J.J. Simplicial zero-point algorithms: A unifying description. J Optim Theory Appl 50, 165–182 (1986). https://doi.org/10.1007/BF00938483

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