A primal-dual integral method in global optimization
Jens Hichert ; Armin Hoffmann ; Huan Xoang Phú ; Rüdiger Reinhardt
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 20 (2000), p. 257-278 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Using the Fenchel conjugate Fc of Phú’s Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:271478 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1015,
     author = {Jens Hichert and Armin Hoffmann and Huan Xoang Ph\'u and R\"udiger Reinhardt},
     title = {A primal-dual integral method in global optimization},
     journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
     volume = {20},
     year = {2000},
     pages = {257-278},
     zbl = {0977.90050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1015}
}

Jens Hichert; Armin Hoffmann; Huan Xoang Phú; Rüdiger Reinhardt. A primal-dual integral method in global optimization. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 20 (2000) pp. 257-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1015/

[000] [1] Soo Hong Chew and Quan Zheng, Integral Global Optimization, Springer, Berlin 1988.

[001] [2] C.A. Floudas and P.M. Pardalos, A Collection of Test Problems for Constrained Global Optimization Algorithms, Springer, Berlin 1990.

[002] [3] J. Hichert, BARLO - Eine Software zur Wesentlichen Globalen Optimierung, Technical Report 17/98, Technische Universität Ilmenau 1998.

[003] [4] J. Hichert, Methoden zur Bestimmung des wesentlichen Supremums mit Anwendung in der globalen Optimierung, PhD thesis, Technische Universität Ilmenau 1999.

[004] [5] J. Hichert, A. Hoffmann, and H.X. Phu, Convergence speed of an integral method for computing the essential supremum, in: I.M. Bomze, T. Csendes, R. Horst and P.M. Pardalos (eds.): Developments in Global Optimization, pp. 153-170, Kluwer Academic Publishers, Dordrecht 1997. | Zbl 0878.65053

[005] [6] J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vol. I (Fundamentals), Springer, Berlin 1993.

[006] [7] J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vol. II (Advanced Theory and Bundle Methods), Springer, Berlin 1993.

[007] [8] http://solon.cma.univie.ac.at/~neum/glopt

[008] [9] P.M. Pardalos, An open global optimization problem on the unit sphere, Journal of Global Optimization 6 (1995), 213. | Zbl 0822.90125

[009] [10] H.X. Phú and A. Hoffmann, Essential supremum and supremum of summable functions, Numerical Functional Analysis and Optimization 17 (1,2) (1996), 167-180. | Zbl 0877.49013

[010] [11] A. Törn and A. Zilinskas, Global Optimization, Springer, Berlin 1989.

[011] [12] Z.B. Zabinsky and R.L. Smith, Pure adaptive search in global optimization, Mathematical Programming 53 (1992), 323-338. | Zbl 0756.90086

[012] [13] Quan Zheng, Integral Global Optimization of Robust Discontinuous Functions, PhD thesis, The Graduate School of Clemson University, Clemson 1992.

[013] [14] Quan Zheng and Deming Zhuang, Integral global minimization: Algorithms, implementations and numerical tests, Journal of Global Optimization 7 (1995), 421-454. | Zbl 0846.90105