Local Tuning in Peano Curves-based Global Optimization Scheme

Abstract

This paper considers one of the methods to account for the local information on the objective function in Lipschitz global optimization problems. In the course of solving such problems, an issue arises regarding estimating the Lipschitz constant of the objective function arises. According to the classic scheme, this constant is a single estimate for the whole search domain. The method of accounting for local properties is based on building estimates of Lipschitz constants for the search subdomains, and has previously been investigated for the one-dimensional case. For solving multidimensional problems, dimension reduction is applied. A multidimensional optimization problem is reduced to a one-dimensional problem, for which the objective function satisfies the Hölder condition. In this paper, the application of building local Hölder constant estimates in reduced multidimensional optimization problems using the same scheme as is used in one-dimensional Lipschitzian problems is considered.