Comparison of dimensionality reduction schemes for derivative-free global optimization algorithms

A common approach to solving global optimization problems is to use univariate optimization algorithms in combination with dimensional reduction schemes. The paper considers five types of Peano-like space-filling curves (evolvents), which are used to reduce the dimension in the derivative-free algorithm of global optimization. The algorithm is univariate and developed within the framework of the information-statistical approach. This work is the first one, where convergence rates and implementations details of these five evolvents are considered together and directly compared. (C) 2018 The Authors. Published by Elsevier B.V.