Ill-conditioning provoked by scaling in univariate global optimization and its handling on the infinity computer

Abstract

Univariate Lipschitz global optimization problems are considered in this contribution. It is shown that in cases, where it is required to solve a scaled problem with very small or very large finite scaling constants, ill-conditioning can be provoked by scaling. It is established that this situation can be avoided using numerical infinities and infinitesimals. For this purpose, a new kind of a supercomputer – the Infinity Computer – that is able to work numerically with finite, infinite and infinitesimal numbers in a unique framework is used. Numerical experiments on benchmark test problems from the literature confirm the obtained results.