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The wait-and-judge scenario approach applied to antenna array design

Author

Listed:
  • Algo Carè

    (University of Brescia)

  • Simone Garatti

    (Politecnico di Milano)

  • Marco C. Campi

    (University of Brescia)

Abstract

The scenario optimisation approach is a methodology for finding solutions to uncertain convex problems by resorting to a sample of data, which are called “scenarios”. In a min–max set-up, the solution delivered by the scenario approach comes with tight probabilistic guarantees on its risk defined as the probability that an empirical cost threshold will be exceeded when the scenario-based solution is adopted. While the standard theory of scenario optimisation has related the risk of the data-based solution to the number of optimisation variables, a more recent approach, called the “wait-and-judge” scenario approach, enables the user to assess the risk of the solution in a data-dependent way, based on the number of decisive scenarios (“support scenarios”). The aim of this paper is to illustrate the potentials of the wait-and-judge approach for min–max sample-based design and we shall consider to this purpose an antenna array design problem.

Suggested Citation

  • Algo Carè & Simone Garatti & Marco C. Campi, 2019. "The wait-and-judge scenario approach applied to antenna array design," Computational Management Science, Springer, vol. 16(3), pages 481-499, July.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:3:d:10.1007_s10287-019-00345-5
    DOI: 10.1007/s10287-019-00345-5
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    References listed on IDEAS

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    1. Algo Carè & Simone Garatti & Marco C. Campi, 2014. "FAST---Fast Algorithm for the Scenario Technique," Operations Research, INFORMS, vol. 62(3), pages 662-671, June.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    4. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    5. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    6. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    7. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    8. Grani A. Hanasusanto & Vladimir Roitch & Daniel Kuhn & Wolfram Wiesemann, 2017. "Ambiguous Joint Chance Constraints Under Mean and Dispersion Information," Operations Research, INFORMS, vol. 65(3), pages 751-767, June.
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    Cited by:

    1. Ritter, Andreas & Widmer, Fabio & Duhr, Pol & Onder, Christopher H., 2022. "Long-term stochastic model predictive control for the energy management of hybrid electric vehicles using Pontryagin’s minimum principle and scenario-based optimization," Applied Energy, Elsevier, vol. 322(C).

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