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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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Patricio Basso (1982) studied this question.
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