Two acceleration mechanisms in verified global optimization

Abstract

Acceleration devices are very important to speed up interval global optimization algorithms. We propose here two techniques which can be applied in addition to other known techniques. Firstly, we propose a test based on the one-dimensional Newton iteration to discard or split the current box. This test is usually cheap and it is likely to be successful when a good approximation of the minimum is known early. The other technique proposed deals with parallelization. We propose to share the task of the manager process among other non-idle processes in such a way that not only one process is responsible for the load balancing. Experimental results presented show that both techniques yield significant improvements in many cases.