On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions

The implementation of global optimization algorithms, using the arithmetic of infinity, is considered. A relatively simple version of implementation is proposed for the algorithms that possess the introduced property of strong homogeneity. It is shown that the P-algorithm and the one-step Bayesian algorithm are strongly homogeneous.Comment: 11 pages, 1 figur

UN SEMPLICE MODO PER TRATTARE LE GRANDEZZE INFINITE ED INFINITESIME

A new computational methodology allowing one to work in a new way with infinities and infinitesimals is presented in this paper. The new approach, among other things, gives the possibility to calculate the number of elements of certain infinite sets, avoids indeterminate forms and various kinds of divergences. This methodology has been used by the author as a starting point in developing a new kind of computer – the Infinity Computer – able to execute computations and to store in its memory not only finite numbers but also infinite and infinitesimal ones