Adaptive nested optimization scheme for multidimensional global search

Methods for solving the multidimensional multiextremal optimization problems using the nested optimization scheme are considered. A novel approach for solving the multidimensional multiextremal problems based on the adaptive nested optimization has been proposed. This approach enables to develop methods of the global optimum search which are more efficient in comparison with the ones on the base of the traditional nested optimization scheme. The new approach provides advantages due to better usage of the information on the problem in the course of optimization. A general scheme of a adaptive nested optimization is described. A theoretical substantiation of the method convergence is given for the case when for solving the univariate subproblems within the nested scheme an information algorithm of global search is used. Results of numerical experiments on the well-known classes of the test multiextremal functions confirming the efficiency of the proposed scheme are presented.

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