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A primal-dual integral method in global optimization

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Abstrakty
EN
Using the Fenchel conjugate $F^c$ 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.
Twórcy
autor
  • Geomagic GmbH, Harbergstr. 73, D-99099 Erfurt, Germany
  • Institute of Mathematics, Technical University Ilmenau, PF 100565, D-98684 Ilmenau, Germany
  • Institute of Mathematics Hanoi, P.O. Box 631 Bo Ho, 10 000 Hanoi, Vietnam
  • Institute of Mathematics, Technical University Ilmenau, PF 100565, D-98684 Ilmenau, Germany
Bibliografia
  • [1] Soo Hong Chew and Quan Zheng, Integral Global Optimization, Springer, Berlin 1988.
  • [2] C.A. Floudas and P.M. Pardalos, A Collection of Test Problems for Constrained Global Optimization Algorithms, Springer, Berlin 1990.
  • [3] J. Hichert, BARLO - Eine Software zur Wesentlichen Globalen Optimierung, Technical Report 17/98, Technische Universität Ilmenau 1998.
  • [4] J. Hichert, Methoden zur Bestimmung des wesentlichen Supremums mit Anwendung in der globalen Optimierung, PhD thesis, Technische Universität Ilmenau 1999.
  • [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.
  • [6] J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vol. I (Fundamentals), Springer, Berlin 1993.
  • [7] J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Vol. II (Advanced Theory and Bundle Methods), Springer, Berlin 1993.
  • [8] http://solon.cma.univie.ac.at/~neum/glopt
  • [9] P.M. Pardalos, An open global optimization problem on the unit sphere, Journal of Global Optimization 6 (1995), 213.
  • [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.
  • [11] A. Törn and A. Zilinskas, Global Optimization, Springer, Berlin 1989.
  • [12] Z.B. Zabinsky and R.L. Smith, Pure adaptive search in global optimization, Mathematical Programming 53 (1992), 323-338.
  • [13] Quan Zheng, Integral Global Optimization of Robust Discontinuous Functions, PhD thesis, The Graduate School of Clemson University, Clemson 1992.
  • [14] Quan Zheng and Deming Zhuang, Integral global minimization: Algorithms, implementations and numerical tests, Journal of Global Optimization 7 (1995), 421-454.
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Bibliografia
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