Towards the analysis of the simulated annealing method in the multiextremal case

Abstract

There are many applications, where the number to be calculated global extrema is large, or even infinite. These problems include, for example, some experimental design problems, the problem of solving large systems of equations, and several others. If this is single extreme of a function of several variables, one of the commonly used numerical algorithms is the Simulated Annealing, which is also successfully used in high volume discrete problems (traveling salesman problem). In discrete problems known, that the method of simulated annealing searches equal global extremes with equal probability. Continuous case still has not been investigated. It was assumed that equal extremes to be found consistently, sharing their neighborhood during the computation. It is not always effective method, especially in the case when multiple extrema fills a certain region in Rn. The results obtained in this article the general outline of the approach to the problem. We give computational examples showing the effectiveness of the approach. It can be used to create programs, algorithms, indicating the localization of the roots of large systems of equations. It can also be noted, that many planning tasks regression experiments are an infinite number of solutions. Refs 4. Figs 5.