Flying elephants: a general method for solving non-differentiable problems

Adilson Elias Xavier () and Vinicius Layter Xavier ()
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Adilson Elias Xavier: Federal University of Rio de Janeiro
Vinicius Layter Xavier: Federal University of Rio de Janeiro

Journal of Heuristics, 2016, vol. 22, issue 4, No 13, 649-664

Abstract: Abstract Flying Elephants (FE) is a generalization and a new interpretation of the Hyperbolic Smoothing approach. The article introduces the fundamental smoothing procedures. It contains a general overview of successful applications of the approach for solving a select set of five important problems, namely: distance geometry, covering, clustering, Fermat–Weber and hub location. For each problem the original non-smooth formulation and the succedaneous completely differentiable one are presented. Computational experiments for all related problems obtained results that exhibited a high level of performance according to all criteria: consistency, robustness and efficiency. For each problem some results to illustrate the performance of FE are also presented.

Keywords: Non-differentiable optimization; Smoothing; Distance geometry; Covering; Clustering; Fermat–Weber problem; Hub location problem (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10732-014-9268-8

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