TY - JOUR
T1 - A Perturbed Quasi-Newton Algorithm for Bound-Constrained Global Optimization
AU - Ziadi , Raouf
AU - Bencherif-Madani , Abdelatif
JO - Journal of Computational Mathematics
VL - 1
SP - 143
EP - 173
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2307-m2023-0016
UR - https://global-sci.org/intro/article_detail/jcm/23533.html
KW - Global optimization, Limited memory BFGS method, Stochastic perturbation, Truncated multivariate double exponential distribution.
AB - <p style="text-align: justify;">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.</p>