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Interval arithmetic in unidimensional signomial programming

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Abstract

This paper applies an interval arithmetic version of Newton's method to unidimensional problems in signomial programming. Unidimensional dual problems occur in engineering design problems formulated as a signomial program with a single degree of difficulty. Unidimensional primal problems are of interest, since many multidimensional search procedures involve unidimensional searches. The interval arithmetic method is guaranteed to generate all the local optima.

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Authors and Affiliations

  1. Physics, Mathematics, and Computer Science Department, Shell Development Company, Houston, Texas

    L. J. Mancini (Research Engineer)

  2. Department of Mechanical Engineering, Stanford University, Stanford, California

    D. J. Wilde (Professor)

Authors
  1. L. J. Mancini
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  2. D. J. Wilde
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Additional information

Communicated by M. Avriel

The authors are grateful to the National Science Foundation for support through a Graduate Fellowship and Grant No. GK-41301.

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Mancini, L.J., Wilde, D.J. Interval arithmetic in unidimensional signomial programming. J Optim Theory Appl 26, 277–289 (1978). https://doi.org/10.1007/BF00933408

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