Software implementation of nonlocal one-dimensional optimization algorithms based on the Holder condition

The problem of one-dimensional search for a global minimum of a nonconvex function 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 experiments to compare the implemented algorithms for various values of the Holder index. An analysis of the performed experiments showed that the generalization of algorithms based on the Holder condition gives in some cases a significant acceleration effect over algorithms based on the Lipschitz condition. During testing the most preferred values of the Holder index and leading algorithms were identified. The conducted experimental studies confirmed the suitability of the implemented modifications for finding the global minimum of the non-convex function of one variable.