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.