Year: 2025
Author: Raouf Ziadi, Abdelatif Bencherif-Madani
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 143–173
Abstract
This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a stochastic descent method where the deterministic sequence, generated by a limited memory BFGS method, is replaced by a sequence of random variables. To enhance the performance of the proposed algorithm and make sure the perturbations lie within the feasible domain, we have developed a novel perturbation technique based on truncating a multivariate double exponential distribution to deal with bound-constrained problems; the theoretical study and the simulation of the developed truncated distribution are also presented. Theoretical results ensure that the proposed method converges almost surely to the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions as well as on some further engineering problems. The numerical comparisons with stochastic and meta-heuristic methods indicate that the suggested algorithm is promising.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2307-m2023-0016
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 143–173
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Global optimization Limited memory BFGS method Stochastic perturbation Truncated multivariate double exponential distribution.