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A Combined Global & Local Search (CGLS) Approach to Global Optimization

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Abstract

This paper presents a general approach that combines global search strategies with local search and attempts to find a global minimum of a real valued function of n variables. It assumes that derivative information is unreliable; consequently, it deals with derivative free algorithms, but derivative information can be easily incorporated. This paper presents a nonmonotone derivative free algorithm and shows numerically that it may converge to a better minimum starting from a local nonglobal minimum. This property is then incorporated into a random population to globalize the algorithm. Convergence to a zero order stationary point is established for nonsmooth convex functions, and convergence to a first order stationary point is established for strictly differentiable functions. Preliminary numerical results are encouraging. A Java implementation that can be run directly from the Web allows the interested reader to get a better insight of the performance of the algorithm on several standard functions. The general framework proposed here, allows the user to incorporate variants of well known global search strategies.

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Authors and Affiliations

  1. Dep. Procesos y Sistemas, Universidad Simón Bolívar, Apartado, 89000, Caracas, Venezuela

    U. M. Garcia-Palomares

  2. Dep. Ingeniería Telemática, ETSI Telecomunicación, Universidade de Vigo, Campus, Apartado, 36310, Vigo, Spain

    U. M. Garcia-Palomares, F. J. Gonzalez-Castaño & J. C. Burguillo-Rial

Authors
  1. U. M. Garcia-Palomares
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  2. F. J. Gonzalez-Castaño
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  3. J. C. Burguillo-Rial
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Correspondence to U. M. Garcia-Palomares.

Additional information

Research done under the cooperation agreement between Universidade de Vigo and Universidad Simón Bolívar.

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Garcia-Palomares, U.M., Gonzalez-Castaño, F.J. & Burguillo-Rial, J.C. A Combined Global & Local Search (CGLS) Approach to Global Optimization. J Glob Optim 34, 409–426 (2006). https://doi.org/10.1007/s10898-005-3249-2

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  • DOI: https://doi.org/10.1007/s10898-005-3249-2

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