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Superlinearly convergent algorithm for min-max problems

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Abstract

Algorithms for solving the problem of minimizing the maximum of a finite number of functions are proposed and analyzed. Quadratic approximations to the functions are employed in the determination of a search direction. Global convergence is proven and it is shown that a quadratic rate of convergence is obtained.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences and Electronics Research Laboratory, University of California, Berkeley, California

    E. Polak (Professor) & J. E. Higgins (Research Assistant)

  2. Department of Electrical Engineering, Imperial College of Science and Technology, London, Great Britain

    D. Q. Mayne (Professor)

Authors
  1. E. Polak
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  2. D. Q. Mayne
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  3. J. E. Higgins
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Additional information

This research was sponsored in part by National Science Foundation Grant ECS-81-21149, Air Force Office of Scientific Research Grant 83-0361, Office of Naval Research Contract N00014-83-K-0602, Semiconductor Research Corporation Contract SRC-82-11-008, State of California MICRO Program, and General Electric Company.

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Polak, E., Mayne, D.Q. & Higgins, J.E. Superlinearly convergent algorithm for min-max problems. J Optim Theory Appl 69, 407–439 (1991). https://doi.org/10.1007/BF00940683

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