a stabilized simulated annealing-based barzilai–borwein method for the solution of unconstrained optimization problems

The barzilai–borwein method offers efficient step sizes for large-scale un-constrained optimization problems. however, it may not guarantee global convergence for nonquadratic objective functions. simulated annealing-based on barzilai–borwein (sabb) method addresses this issue by in-corporating a simulated annealing rule. this work proposes a novel step-size strategy for the sabb method, referred to as the sabbm method. furthermore, we introduce two stabilized variants: sabbstab and sabbmstab. sabbstab combines a simulated annealing rule with a sta-bilization step to ensure convergence. sabbmstab builds upon sabbstab, incorporating the modified step size derived from the sabbm method. the effectiveness and competitiveness of the proposed methods are demon-strated through numerical experiments on cuter benchmark problems.