Enclosure methods for multivariate differentiable functions and application to global optimization

Journal of Universal Computer Science

Volumn 4, Issue 6, 1998, Pages 589-603

  Messine, Frédéric ^a   Lagouanelle, Jean Louis ^b  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b IRIT   (France)

Author keywords

Branch and bound algorithm; Global optimization; Interval arithmetic; Multivariate functions; Polyhedral cone; Taylor's expansion

Indexed keywords

EID: 10044257404     PISSN: 0958695X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. G. ALEFELD Bounding the Slope of Polynomial Operators and some Applications, Computing : 26 (227-237) - (1980).
2. K. DU, R. B. KEARFOTT The Cluster Problem in Multivariate Global Optimization, Journal of Global Optimization : 10 (27-32) - (1996).
3. E. HANSEN Global optimization Using Interval Analysis, MARCEL DEKKER, Inc. 270 Madison Avenue, New York, New York 10016 - (1992).
4. K. ICHIDA, Y. FUJII An Interval Arithmetic Method for Global Optimization, Computing : 23 (85-97) - (1979).
5. P. HANSEN, B. JAUMARD, J. XIONG Decomposition and Interval Arithmetic Applied to Global Minimization of Polynomial and Rational Functions, Journal of Global Optimization : 3 (421-437) - (1992).
6. R. B. KEARFOTT Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, Boston, London - (1996).
7. J.L. LAGOUANELLE, F. MESSINE Algorithme d'encadrement de l'optimum global d'une fonction différentiable, Compte Rendu à l'Académie des Sciences, Numerical Analysis, T. 326, Série I, (1998).
8. R.H. MLADINEO An Algorithm for Finding the Global Maximum of a Multimodal, Multivariate Function, Mathematical Programming : 34 (188-200) - (1986).
9. R. E. MOORE Interval Analysts, Prentice Hall, Inc. Englewood Cliffs, N.J. (1966).
10. H. RATSCHEK, J. ROKNE New Computer Methods for Global optimization, ELLIS HORWOOD LIMITED Market Cross House, Cooper Street, Chichester, West Sussex, PO19 1EB, England - (1988).
11. V. VISWESWARAN, C.A. FLOUDAS Uncontramed and Constrained Global Optimization of Polynomial Function in one Variable, Journal of Global Optimization: 2 (73-99) - (1992).