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Bibliographic description:
Sorokovikov P. S.
SOFTWARE IMPLEMENTATION OF NONLOCAL ONE-DIMENSIONAL OPTIMIZATION ALGORITHMS BASED ON THE HÖLDER CONDITION // BSU bulletin. Mathematics, Informatics. - 2019. №4. . - С. 40-56.
Title:
SOFTWARE IMPLEMENTATION OF NONLOCAL ONE-DIMENSIONAL OPTIMIZATION ALGORITHMS BASED ON THE HÖLDER CONDITION
Financing:
Работа выполнена при финансовой поддержке РФФИ, проект №19-37-90065.
Codes:
DOI: 10.18101/2304-5728-2019-4-40-56UDK: 519.853
Annotation:
The problem of one-dimensional search for a global minimum of a nonconvex func- tion often appears as an auxiliary for solving multidimensional optimization problems. For many years, nonlocal one-dimensional optimization methods have been developed by a number of specialists from Russia and foreign countries. The article considers the proposed modifications of nonlocal one-dimensional search algorithms based on the Hölder condition. These modifications are implemented as an algorithms library and integrated into a single software package. The library includes modifications of Yu. G. Evtushenko’s, R. G. Strongin’s methods and a combined algorithm based on the Strongin’s method of "parabolas". We have made multivariant computational experi- ments to compare the implemented algorithms for various values of the Hölder index. An analysis of the performed experiments showed that the generalization of algorithms based on the Hölder condition gives in some cases a significant acceleration effect over algorithms based on the Lipschitz condition. During testing the most preferred values of the Hölder index and leading algorithms were identified. The conducted experimen- tal studies confirmed the suitability of the implemented modifications for finding the global minimum of the non-convex function of one variable.
Keywords:
nonlocal one-dimensional search; the Hölder condition; Evtushenko’s method; Strongin’s method; global minimum; algorithms library; software implementa- tion.
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