کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4639570 | 1341239 | 2012 | 13 صفحه PDF | دانلود رایگان |

A global optimization problem is studied where the objective function f(x)f(x) is a multidimensional black-box function and its gradient f′(x)f′(x) satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant KK. Different methods for solving this problem by using an a priori given estimate of KK, its adaptive estimates, and adaptive estimates of local Lipschitz constants are known in the literature. Recently, the authors have proposed a one-dimensional algorithm working with multiple estimates of the Lipschitz constant for f′(x)f′(x) (the existence of such an algorithm was a challenge for 15 years). In this paper, a new multidimensional geometric method evolving the ideas of this one-dimensional scheme and using an efficient one-point-based partitioning strategy is proposed. Numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular DIRECT-based methods.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 16, October 2012, Pages 4042–4054