Application of lissajous curves to box optimization problems

Abstract

This work addresses deterministic global optimization methods for multivariate Lipschitz functions. We focused on one-dimensional covering methods (Piyavskii-Shubert and Evtushenko). To extend these methods to the multidimensional case, we used the reducing transformation with α-dense curves of the Lissajous type. Coupling these curves with classical algorithms enabled solving two-dimensional problems. The results show the superiority of the hybrid Evtushenko-Lissajous method.