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Nonlinear programming using minimax techniques

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Abstract

A minimax approach to nonlinear programming is presented. The original nonlinear programming problem is formulated as an unconstrained minimax problem. Under reasonable restrictions, it is shown that a point satisfying the necessary conditions for a minimax optimum also satisfies the Kuhn-Tucker necessary conditions for the original problem. A leastpth type of objective function for minimization with extremely large values ofp is proposed to solve the problem. Several numerical examples compare the present approach with the well-known SUMT method of Fiacco and McCormick. In both cases, a recent minimization algorithm by Fletcher is used.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, McMaster University, Hamilton, Ontario, Canada

    J. W. Bandler (Associate Professor of Electrical Engineering)

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada

    C. Charalambous (Post-Doctoral Fellow)

Authors
  1. J. W. Bandler
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  2. C. Charalambous
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Additional information

Communicated by G. L. Nemhauser

This paper is based on work presented at the 5th Hawaii International Conference on System Sciences, Honolulu, Hawaii, 1972. The authors are greatly indebted to V. K. Jha for his programming assistance and J. H. K. Chen who obtained some of the numerical results. This work was supported in part by the National Research Council of Canada under Grant No. A7239, by a Frederick Gardner Cottrell Grant from the Research Corporation, and through facilities and support from the Communications Research Laboratory of McMaster University.

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Bandler, J.W., Charalambous, C. Nonlinear programming using minimax techniques. J Optim Theory Appl 13, 607–619 (1974). https://doi.org/10.1007/BF00933620

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