A combined global & local search (CGLS) approach to global optimization 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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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Gnandt, Christian; Callies, Rainer: CGRS -- an advanced hybrid method for global optimization of continuous functions closely coupling extended random search and conjugate gradient method (2018)
- Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
- Custódio, A.L.; Madeira, J.F.A.: GLODS: global and local optimization using direct search (2015)
- Zhou, Qinghua; Li, Yan; Ha, Minghu: Constructing composite search directions with parameters in quadratic interpolation models (2011)
- Olenšek, Jernej; Bűrmen, Árpád; Puhan, Janez; Tuma, Tadej: DESA: a new hybrid global optimization method and its application to analog integrated circuit sizing (2009)
- González-Castaño, Francisco J.; Costa-Montenegro, Enrique; Burguillo-Rial, Juan C.; García-Palomares, Ubaldo: Outdoor WLAN planning via non-monotone derivative-free optimization: Algorithm adaptation and case study (2008)
- Lee, Chi-Hoon; Zaïane, Osmar R.; Park, Ho-Hyun; Huang, Jiayuan; Greiner, Russell: Clustering high dimensional data: A graph-based relaxed optimization approach (2008) ioport
- Garcia-Palomares, U.M.; Gonzalez-Castaño, F.J.; Burguillo-Rial, J.C.: A combined global & local search (CGLS) approach to global optimization (2006)