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Global Optimization Requires Global Information

Author

Listed:
  • C. P. Stephens

    (niversity of Canterbury)

  • W. Baritompa

    (University of Canterbury)

Abstract

There are many global optimization algorithms which do not use global information. We broaden previous results, showing limitations on such algorithms, even if allowed to run forever. We show that deterministic algorithms must sample a dense set to find the global optimum value and can never be guaranteed to converge only to global optimizers. Further, analogous results show that introducing a stochastic element does not overcome these limitations. An example is simulated annealing in practice. Our results show that there are functions for which the probability of success is arbitrarily small.

Suggested Citation

  • C. P. Stephens & W. Baritompa, 1998. "Global Optimization Requires Global Information," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 575-588, March.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:3:d:10.1023_a:1022612511618
    DOI: 10.1023/A:1022612511618
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    References listed on IDEAS

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    1. Francisco J. Solis & Roger J.-B. Wets, 1981. "Minimization by Random Search Techniques," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 19-30, February.
    2. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
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    Cited by:

    1. Alberto Lovison, 2013. "Global search perspectives for multiobjective optimization," Journal of Global Optimization, Springer, vol. 57(2), pages 385-398, October.
    2. Regis, Rommel G., 2010. "Convergence guarantees for generalized adaptive stochastic search methods for continuous global optimization," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1187-1202, December.
    3. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    4. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
    5. Rommel G. Regis, 2016. "On the Convergence of Adaptive Stochastic Search Methods for Constrained and Multi-objective Black-Box Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 932-959, September.

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