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A New Nonmonotone Trust Region Algorithm Based on Simulated Annealing and Barzilai–Borwein Methods for Unconstrained Optimization

Author

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  • Seyed Hamzeh Mirzaei

    (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran)

  • Ali Ashrafi

    (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran)

Abstract

In this paper, a new nonmonotone trust region algorithm based on a novel combination of a nonmonotone strategy, a modified Metropolis criterion, and the Barzilai–Borwein step size is proposed. The proposed algorithm uses the reciprocal of Barzilai–Borwein step size to approximate the Hessian matrix of the objective function in the trust region subproblems and accepts some bad solutions according to the modified Metropolis criterion based on the simulated annealing idea. Under some mild assumptions, the global convergence of the algorithm is established. Some preliminary numerical results indicate that the new algorithm performs well with high efficiency.

Suggested Citation

  • Seyed Hamzeh Mirzaei & Ali Ashrafi, 2025. "A New Nonmonotone Trust Region Algorithm Based on Simulated Annealing and Barzilai–Borwein Methods for Unconstrained Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 42(05), pages 1-24, October.
    • Handle: RePEc:wsi:apjorx:v:42:y:2025:i:05:n:s0217595925500010
    DOI: 10.1142/S0217595925500010
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