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A subgradient algorithm for certain minimax and minisum problems

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Abstract

We present a subgradient algorithm for minimizing the maximum of a finite collection of functions. It is assumed that each function is the sum of a finite collection of basic convex functions and that the number of different subgradient sets associated with nondifferentiable points of each basic function is finite on any bounded set. Problems belonging to this class include the linear approximation problem and both the minimax and minisum problems of location theory. Convergence of the algorithm to an epsilon-optimal solution is proven and its effectiveness is demonstrated by solving a number of location problems and linear approximation problems.

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Authors and Affiliations

  1. Paris, France

    J. A. Chatelon

  2. University of Florida, Gainesville, FL., USA

    D. W. Hearn & T. J. Lowe

Authors
  1. J. A. Chatelon
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  2. D. W. Hearn
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  3. T. J. Lowe
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Additional information

This research was partially supported by the Army Research Office, Triangle Park, NC, under contract number DAH-CO4-75-G-0150, and by NSF grants ENG 16-24294 and ENG 75-10225.

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Chatelon, J.A., Hearn, D.W. & Lowe, T.J. A subgradient algorithm for certain minimax and minisum problems. Mathematical Programming 15, 130–145 (1978). https://doi.org/10.1007/BF01609012

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  • DOI: https://doi.org/10.1007/BF01609012

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