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Efficient Solution of Maximum-Entropy Sampling Problems

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  • Kurt M. Anstreicher

    (Department of Business Analytics, University of Iowa, Iowa City, Iowa 52242)

Abstract

We consider a new approach for the maximum-entropy sampling problem (MESP) that is based on bounds obtained by maximizing a function of the form ldet M ( x ) over linear constraints, where M ( x ) is linear in the n -vector x . These bounds can be computed very efficiently and are superior to all previously known bounds for MESP on most benchmark test problems. A branch-and-bound algorithm using the new bounds solves challenging instances of MESP to optimality for the first time.

Suggested Citation

  • Kurt M. Anstreicher, 2020. "Efficient Solution of Maximum-Entropy Sampling Problems," Operations Research, INFORMS, vol. 68(6), pages 1826-1835, November.
    • Handle: RePEc:inm:oropre:v:68:y:2020:i:6:p:1826-1835
    DOI: 10.1287/opre.2019.1962
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    References listed on IDEAS

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    1. Chun-Wa Ko & Jon Lee & Maurice Queyranne, 1995. "An Exact Algorithm for Maximum Entropy Sampling," Operations Research, INFORMS, vol. 43(4), pages 684-691, August.
    2. Kim-Chuan Toh & Michael J. Todd & Reha H. Tütüncü, 2012. "On the Implementation and Usage of SDPT3 – A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 715-754, Springer.
    3. ANSTREICHER, Kurt M. & FAMPA, Marcia & LEE, Jon & WILLIAMS, Joy, 1999. "Using continuous nonlinear relaxations to solve constrained maximum-entropy sampling problems," LIDAM Reprints CORE 1412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Jon Lee, 1998. "Constrained Maximum-Entropy Sampling," Operations Research, INFORMS, vol. 46(5), pages 655-664, October.
    5. Kurt M. Anstreicher, 2018. "Maximum-entropy sampling and the Boolean quadric polytope," Journal of Global Optimization, Springer, vol. 72(4), pages 603-618, December.
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    Cited by:

    1. Zhongzhu Chen & Marcia Fampa & Jon Lee, 2023. "On Computing with Some Convex Relaxations for the Maximum-Entropy Sampling Problem," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 368-385, March.

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