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 unconstrained optimization problems. However, it may not guarantee global convergence for nonquadratic objective functions. Simulated annealingbased on Barzilai-Borwein (SABB) method addresses this issue by incorporating 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 stabilization 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 demonstrated through numerical experiments on CUTEr benchmark problems. [ABSTRACT FROM AUTHOR]

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