Optimal multisections in interval branch-and-bound methods of global optimization

Journal of Global Optimization

Volumn 30, Issue 1, 2004, Pages 23-38

  Lagouanelle, Jean Louis ^a   Soubry, Gérard ^b  

^a IRIT   (France)

^b UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

Centered form; Global optimization; Interval branch and bound method; Optimal lower bound; Optimal multisection

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL GEOMETRY; DECOMPOSITION; FUNCTIONS; OPTIMAL CONTROL SYSTEMS; SET THEORY;

CENTERED FORM; INTERVAL BRANCH-AND-BOUND METHOD; OPTIMAL LOWER BOUND; OPTIMAL MULTISECTION;

GLOBAL OPTIMIZATION;

EID: 18244396328     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOGO.0000049095.55259.61     Document Type: Article

References (24)

1. Alefeld, G. and Herzberger, J. (1983), Introduction to Interval Computations, Academic Press, New York.
2. Baumann, E. (1988), Optimal centered forms, BIT 28(1), 80-87.
3. Berger, M. (1968), Perspectives in Nonlinearity, W.A. Benjamin, Inc.
4. Csendes, T., Market, M.C. and Csallner, A.E. (1997), Multisections in Interval Methods for Global Optimization, Communication in S.C.A.N.97, International GAMM/IMACS Symposium, Lyon, Sept. 1997.
5. Evtushenko, Y.G. (1971), Numerical methods for finding global extrema (case of non-uniform mesh), USSR Computational Mathematical Physics 11, 38-54.
6. Evtushenko, Y.G., Potapov, M.A. and Korotkich, V.V. (1992), Numerical methods for global optimization. In: Floudas, C.A. and Pardalos, P.M. (eds), Recent Advances in Global Optimization, Princeton Series in Computer Science, pp. 274-297.
7. Griewank, A. (2000), Evaluating derivatives, SIAM series on Frontiers in Applied Mathematics.
8. Hansen, E.R. (1992), Global Optimization Using Interval Analysis, Marcel Dekker, New York.
9. Hansen, P. and Jaumard, B. (1995), Lipschitz optimization. In: Horst, R. and Pardalos, P.M. (eds), Handbook of Global Optimization, Kluwer Academic Publishers, pp. 407-493.
10. Kearfott, R.B. (1996), Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers.
11. Lagouanelle, J.L. (2000), Kite Algorithm: A New Global Interval Method from Linear Evaluations, communication at S.C.A.N.2000, International GAMM/IMACS Symposium, Karlsruhe, Sept. 2000.
12. Lagouanelle, J.L. Algorithme du Cerf-volant en Optimization Globale par Intervalles, Technical Report RT/APO/01/2, IRIT, Toulouse, France.
13. Lagouanelle, J.L. and Messine, F. (1998), Algorithme d'Encadrement de l'Optimum d'une Fonction Differentiable, C.R.A.S. t.326, Serie I, 629-632.
14. Neumaier, A. (1990), Interval Methods for Systems of Equations, Cambridge University Press.
15. Ortega, J. and Rheinboldt, W. (1970), Iterative Solutions of Nonlinear Equations, Academic Press, New York.
16. Pinter, J. (1988), Branch-and-bound algorithms for solving global optimization problems with Lipschitzian structure. Optimization 19, 101-110.
17. Piyavski, S.A. (1972), An algorithm for finding the absolute extremum of a function, USSR Computational Mathematical Physics 12, 57-67.
18. Rail, L.B. (1981), Automatic differentiation: Techniques and applications, Lectures Notes in Comput. Sci. 120, Springer, Berlin.
19. Ratschek, H. and Rokne, J. (1988), New Computer methods for Global Optimization, Wiley, New York.
20. Ratschek, H. and Rokne, J. (1995), Interval methods. In: Horst, R. and Pardalos, P.M. (eds), Handbook of Global Optimization, Kluwer Academic Publushers, Dordrecht, pp. 751-828.
21. Ratz, D. (2000), Non Smooth Global Optimization, communication at S.C.A.N. 2000, International GAMM/IMACS Symposium, Karlsruhe, Sept. 2000.
22. Schwartz, J.T. (1969), Nonlinear Functional Analysis, Gordon and Breach Science Publishers.
23. Vinko, T., Lagouanelle, J.L. and Csendes, T. (2001), A New Inclusion Function for Optimization: Kite-The One Dimensional Case, submitted, Oct. 2001.
24. Visweswaran, V. and Floudas, C.A. (1992), Global optimization of problems with polynomial functions in one variable. In: Floudas, C.A. and Pardalos, P.M. (eds), Recent Advances in Global Optimization, Princeton Series in Comp. Sci.