Lipschitz gradients for global optimization in a one-point-based partitioning scheme

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Sergeyev, Yaroslav D.¹ 

[1] DEIS Univ Calabria, I-87036 Arcavacata Di Rende, CS, Italy

关键词: Global optimization;    Lipschitz gradients;    Set of Lipschitz constants;    Geometric algorithms;   

DOI  :  10.1016/j.cam.2012.02.020

来源: Elsevier

【 摘 要 】

A global optimization problem is studied where the objective function f(x) is a multidimensional black-box function and its gradient f'(x) satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant K. Different methods for solving this problem by using an a priori given estimate of K, 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) (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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free