## 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

### Citations:

Zbl 0417.65022; Zbl 0251.65052; Zbl 0483.65038
Full Text:

### References:

 [1] Asaithambi, N. S., Shen, Z., Moore, R. E.: On computing the range of values. Computing28, 225–237 (1982). · Zbl 0473.65004 [2] Basso, P: Iterative methods for the localization of the maximum. SIAM J. Number. Anal.19, 781–792 (1982). · Zbl 0483.65038 [3] Hansen, E.: Global optimization using interval analysis – a the one-dimensional case. J. Optim. Theory Appl.29, 331–344 (1979). · Zbl 0388.65023 [4] Hansen, E.: Global optimization using interval analysis – the multi-dimensional case. Numer. Math.34, 247–270 (1980). · Zbl 0442.65052 [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
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