×

zbMATH — the first resource for mathematics

An interval version of Shubert’s iterative method for the localization of the global maximum. (English) Zbl 0602.65040
Using the “bisection rule” of R. E. Moore [Methods and applications of interval analysis. Philadelphia: SIAM (1979; Zbl 0417.65022)], a simple algorithm is given which is an interval version of Shubert’s iterative method [B. O. Shubert, SIAM J. Numer. Anal. 9, 379–388 (1972; Zbl 0251.65052)] for seeking the global maximum of a function of a single variable defined on a closed interval \([a,b]\). The algorithm which is always convergent can be easily extended to the higher dimensional case. It seems much simpler than and produces results comparable to that proposed by Shubert and P. Basso [SIAM J. Numer. Anal. 19, 781–792 (1982; Zbl 0483.65038)].

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
65G30 Interval and finite arithmetic
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Asaithambi, N. S., Shen, Z., Moore, R. E.: On computing the range of values. Computing28, 225–237 (1982). · Zbl 0473.65004 · doi:10.1007/BF02241750
[2] Basso, P: Iterative methods for the localization of the maximum. SIAM J. Number. Anal.19, 781–792 (1982). · Zbl 0483.65038 · doi:10.1137/0719054
[3] Hansen, E.: Global optimization using interval analysis – a the one-dimensional case. J. Optim. Theory Appl.29, 331–344 (1979). · Zbl 0388.65023 · doi:10.1007/BF00933139
[4] Hansen, E.: Global optimization using interval analysis – the multi-dimensional case. Numer. Math.34, 247–270 (1980). · Zbl 0442.65052 · doi:10.1007/BF01396702
[5] Moore, R. E.: Methods and applications of interval analysis. SIAM Philadelphia, 1979.
[6] Ratschek, H.: Inclusion functions and global optimization. Mathematical Programming, to appear (1985). · Zbl 0579.90082
[7] Shubert, B. O.: A sequential method seeking the global maximum of a function. SIAM J. Number. Anal.9, 379–388 (1972). · Zbl 0251.65052 · doi:10.1137/0709036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.