APPLICATION OF THE METHOD OF DIVIDING A SEGMENT IN HALF IN GLOBAL OPTIMIZATION BASED ON AN AUXILIARY FUNCTION - Tutkusheva, Zh.S. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
In this paper, the problem of global optimization of a smooth function of several variables given on a cuboid is considered. The search for a solution is carried out using an auxiliary function obtained by a special transformation of the objective function. An auxiliary function is a function of one variable, the zero of which coincides with the value of the global minimum of the objective function. Therefore, to solve the problem, the method of dividing the segment in half was used. The results of this work were revealed on the basis of a large number of computational experiments conducted on test functions using the proposed method. These results are formulated in the form of three theorems and theoretically proved. In the first theorem, conditions are defined that indicate the interval in which the value of the global minimum is located. The second theorem expresses the convergence of the iterative sequence to the value of the global minimum. In the third theorem, the linear convergence rate of the iterative procedure is established. As an example, the multiextremal Eckley function of two variables defined in a square centered at the origin is considered.