A Perturbed Quasi-Newton Algorithm for Bound-Constrained Global Optimization (Journal of Computational Mathematics, 2024)
This paper presents a stochastic modification of a limited memory BFGS method tosolve bound-constrained global minimization problems with a differentiable cost functionwith no further smoothness. The approach is a stochastic descent method where thedeterministic sequence, generated by a limited memory BFGS method, is replaced bya sequence of random variables. To enhance the performance of the proposed algorithmand make sure the perturbations lie within the feasible domain, we have developed a novelperturbation technique based on truncating a multivariate double exponential distributionto deal with bound-constrained problems; the theoretical study and the simulation of thedeveloped truncated distribution are also presented. Theoretical results ensure that theproposed method converges almost surely to the global minimum. The performance of thealgorithm is demonstrated through numerical experiments on some typical test functions aswell as on some further engineering problems. The numerical comparisons with stochasticand meta-heuristic methods indicate that the suggested algorithm is promising.