Global Optimization with Higher Order Inclusion Function Forms Part 1: A Combined Taylor-Bernstein Form

摘要

Recently, two versions of the so-called Taylor-Bernstein (TB) form having the property of higher order convergence were proposed in [5] and [10]. However, in many application problems, both these TB forms encounter difficulties in computing the range enclosures for some domain widths, due to excessive memory and/or time requirements. In this paper, we present a combined TB form that is more successful in computing the range enclosures as the domain shrinks from large to small widths. We test and compare the performance of the proposed form with those of the existing TB forms, the Taylor model of Berz et al. [1], and the simple natural inclusion function form. For the testing, we consider six benchmark examples with dimensions varying from 1 to 6. The results of the tests show that the proposed combined TB form is indeed more effective than the existing TB forms and the Taylor model, over the entire range of domain widths considered.