Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

[1] M. Bader, Space Filling Curves. An Introduction with Applications in Scientific Computing, Springer Verlag, 2013. Search in Google Scholar

[2] A. R. Butz, Space filling curves and mathematical programming, Information and control 12 (4) (1968), 313-330. Search in Google Scholar

[3] Y. Cherruault, G. Mora, Optimisation Globale Theorie des Courbes Alpha-Denses, Economica Paris, 2005. Search in Google Scholar

[4] P. J. Davis, P. Rabinowitz, Methods of numerical integration, Second Edition, Dover Publications, New York, 2007. Search in Google Scholar

[5] G. Garcia, G. Mora, D. A. Redtwitz, Box-Counting Dimension Computed By α-Dense Curves, Fractals 25 (5) (2017), 1750039. Search in Google Scholar

[6] D. Guettal, A. Ziadi, Reducing Transformation and Global Optimization, Applied Mathematics and Computation 218 (2012), 5848-5860. Search in Google Scholar

[7] D. Guettal, E cacité et fiabilité des méthodes utilisant l’approche branch-and-bound pour l’optimisation globale non convexe. Thèse de Doctorat en Sciences, Université Ferhat Abbas, Sétif, Algeria, 2014. Search in Google Scholar

[8] T. X. He, Dimensionality Reducing Expansion of Multivariable Integration, Birkh¨auser, Boston, 2001. Search in Google Scholar

[9] G. Mora, Y. Cherruault, A. Benabidallah, Y. Tourbier, Approximating Multiple Integrals via Dense Curves, Kybernetes 31 (2) (2002), 292-304. Search in Google Scholar

[10] M. Rahal, A. Ziadi, R. Ellaia, Generating -dense curves in non-convex sets to solve a class of non-smooth constrained global optimization, Croatian Operational Research Review 10 (2019), 289-314. Search in Google Scholar

[11] H. Sagan, Space-filling curves, Springer Verlag, 1994. Search in Google Scholar

[12] A. Ziadi, Y. Cherruault, Generation of α-dense curves in a cube of ℝⁿ, Kybernetes 27 (4) (1998), 416-425. Search in Google Scholar

[13] A. Ziadi, Y. Cherruault, Generation of α-dense curves and application to global optimization, Kybernetes 27 (1) (2000), 71-82. Search in Google Scholar

[14] A. Ziadi, D. Guettal, Y. Cherruault, Global optimization: The Alienor mixed method with Piyavskii-Shubert technique, Kybernetes 34 (7/8) (2005), 1049-1058. Search in Google Scholar

[15] R. Ziadi, R., A. Bencherif-Madani, R. Ellaia, Continuous global optimization through the generation of parametric curves, Applied Mathematics and Computation 282 (2016), 65-83. Search in Google Scholar