Possible Extensions to the DIRECT Global Optimization Algorithm Based on Space-Filling and Diagonal Curves

Dimitri E. Kvasov;Daniela Lera

Secondo

;Yaroslav D. Sergeyev

2023-01-01

---

Abstract

In this paper, the Lipschitz global optimization problem is considered both in the cases of non-differentiable and differentiable objective functions over hyperintervals. It is shown that space-filling curves can be successfully used to extend promising one-dimensional methods to the multidimensional case. In particular, several DIRECT-based algorithms using Peano-Hilbert space-filling curves and adaptive diagonal curves are surveyed.