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On the minimal length curve that densifies the square

Gaspar Mora, Yves Cherruault

Kybernetes

ISSN: 0368-492X

Article publication date: 1 December 1999

120

Abstract

This paper deals with the existence of a curve of minimal length, expressed in parametric coordinates, which densifies the square J2=≤ft [ −1,1\right ] × ≤ft [ −1,1\right ] \ with a given degree of density α. Nevertheless, the same problem has no solution if we consider the family of curves defined by means of the graphics of continuous and rectifiable functions f: J→ J. Their consequences on the approximation method to the global optimization are also derived.

Keywords

Citation

Mora, G. and Cherruault, Y. (1999), "On the minimal length curve that densifies the square", Kybernetes, Vol. 28 No. 9, pp. 1054-1064. https://doi.org/10.1108/03684929910300277

Publisher

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MCB UP Ltd

Copyright © 1999, MCB UP Limited

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