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Iterative Methods for the Localization of the Global Maximum

Patricio Basso
SIAM Journal on Numerical Analysis
Vol. 19, No. 4 (Aug., 1982), pp. 781-792
Stable URL: http://www.jstor.org/stable/2157032
Page Count: 12
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Iterative Methods for the Localization of the Global Maximum
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Abstract

Methods for the search of a maximum utilizing a sequence of majorants to generate a sequence of localizations are analyzed. Necessary and sufficient conditions for the convergence of this sequence are given. The case of Lipschitz-continuous functions is studied in detail and an analogy with iterative and relaxation methods for the solution of a system of linear equations is made. Methods of Jacobi, Gauss-Seidel and chaotic type are proposed.

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