Acceleration Tools for Diagonal Information Global Optimization Algorithms

In this paper we face a classical global optimization problem—minimization of a multiextremal multidimensional Lipschitz function over a hyperinterval. We introduce two new diagonal global optimization algorithms unifying the power of the following three approaches: efficient univariate information global optimization methods, diagonal approach for generalizing univariate algorithms to the multidimensional case, and local tuning on the behaviour of the objective function (estimates of the local Lipschitz constants over different subregions) during the global search. Global convergence conditions of a new type are established for the diagonal information methods. The new algorithms demonstrate quite satisfactory performance in comparison with the diagonal methods using only global information about the Lipschitz constant.

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