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Discrete optimization on a multivariable boolean lattice

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Abstract

Consider the problem of finding the minimum value of a scalar objective function whose arguments are theN components of 2N vector elements partially ordered as a Boolean lattice. If the function is strictly decreasing along any shortest path from the minimum point to its logical complement, then the minimum can be located precisely after sequential measurement of the objective function atN + 1 points. This result suggests a new line of research on discrete optimization problems.

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References

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Author notes

  1. J. M. Sanchez-Anton

    Present address: IBM Corporation, Madrid, Spain

Authors and Affiliations

  1. Department of Chemical Engineering, Stanford University, 94305, Stanford, Calif., USA

    D. J. Wilde & J. M. Sanchez-Anton

Authors
  1. D. J. Wilde
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  2. J. M. Sanchez-Anton
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Additional information

This research was supported in part by U.S. Office of Saline Water Grant No. 699.

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Wilde, D.J., Sanchez-Anton, J.M. Discrete optimization on a multivariable boolean lattice. Mathematical Programming 1, 301–306 (1971). https://doi.org/10.1007/BF01584094

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  • DOI: https://doi.org/10.1007/BF01584094

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