A stabilized simulated annealing based Barzilai-Borwein method for the solution of unconstrained optimization problems

Articles in Press

Document Type : Research Article

Authors

• Hitarth Sharma
• Rupaj Kumar Nayak

Department of Mathematics, International Institute of Information Technology, Bhubaneswar, Odisha, India, 751029

10.22067/ijnao.2024.86481.1379

Abstract

The Barzilai-Borwein (BB) method offers efficient step sizes for large-scale unconstrained optimization problems. However, it may not guarantee global convergence for non-quadratic objective functions. The simulated annealing-based 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.

Keywords

• Unconstrained optimization
• Barzilai-Borwein method
• Simulated annealing method
• Stabilized BB method

Main Subjects

• Optimization

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