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Functional Optimization Through Semilocal Approximate Minimization

Author

Listed:
  • Cristiano Cervellera

    (Istituto di Studi sui Sistemi Intelligenti per l'Automazione, Consiglio Nazionale delle Ricerche, 16149 Genova, Italy)

  • Danilo Macciò

    (Istituto di Studi sui Sistemi Intelligenti per l'Automazione, Consiglio Nazionale delle Ricerche, 16149 Genova, Italy)

  • Marco Muselli

    (Istituto di Elettronica e di Ingegneria dell'Informazione e delle Telecomunicazioni, Consiglio Nazionale delle Ricerche, 16149 Genova, Italy)

Abstract

An approach based on semilocal approximation is introduced for the solution of a general class of operations research problems, such as Markovian decision problems, multistage optimal control, and maximum-likelihood estimation. Because it is extremely hard to derive analytical solutions that minimize the cost in most instances of the problem, we must look for approximate solutions. Here, it is shown that good solutions can be obtained with a moderate computational effort by exploiting properties of semilocal approximation through kernel models and efficient sampling of the state space. The convergence of the proposed method, called semilocal approximate minimization (SLAM), is discussed, and the consistency of the solution is derived. Simulation results show the efficiency of SLAM, also through its application to a classic operations research problem, i.e., inventory forecasting.

Suggested Citation

  • Cristiano Cervellera & Danilo Macciò & Marco Muselli, 2010. "Functional Optimization Through Semilocal Approximate Minimization," Operations Research, INFORMS, vol. 58(5), pages 1491-1504, October.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:5:p:1491-1504
    DOI: 10.1287/opre.1090.0804
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    References listed on IDEAS

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    1. Victoria C. P. Chen & David Ruppert & Christine A. Shoemaker, 1999. "Applying Experimental Design and Regression Splines to High-Dimensional Continuous-State Stochastic Dynamic Programming," Operations Research, INFORMS, vol. 47(1), pages 38-53, February.
    2. R. Zoppoli & M. Sanguineti & T. Parisini, 2002. "Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 403-440, February.
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    1. Zéphyr, Luckny & Lang, Pascal & Lamond, Bernard F. & Côté, Pascal, 2017. "Approximate stochastic dynamic programming for hydroelectric production planning," European Journal of Operational Research, Elsevier, vol. 262(2), pages 586-601.

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