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An Improved Non-Monotonic Adaptive Trust Region Algorithm for Unconstrained Optimization

Author

Listed:
  • Mingming Xu

    (School of Mathematics and Physics, Yibin University, Yibin 644000, China)

  • Quanxin Zhu

    (School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China)

  • Hongying Xiao

    (School of Mathematics and Physics, Yibin University, Yibin 644000, China)

Abstract

The trust region method is an effective method for solving unconstrained optimization problems. Incorrectly updating the rules of the trust region radius will increase the number of iterations and affect the calculation efficiency. In order to obtain an effective radius for the trust region, an adaptive radius updating criterion is proposed based on the gradient of the current iteration point and the eigenvalue of the Hessian matrix which avoids calculating the inverse of the Hessian matrix during radius updating. This approach reduces the computation time and enhances the algorithm’s performance. On this basis, we apply adaptive radius and non-monotonic techniques to the trust region algorithm and propose an improved non-monotonic adaptive trust region algorithm. Under proper assumptions, the convergence of the algorithm is analyzed. Numerical experiments confirm that the suggested algorithm is effective.

Suggested Citation

  • Mingming Xu & Quanxin Zhu & Hongying Xiao, 2024. "An Improved Non-Monotonic Adaptive Trust Region Algorithm for Unconstrained Optimization," Mathematics, MDPI, vol. 12(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3398-:d:1510363
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    References listed on IDEAS

    as
    1. Jianjun Liu & Xiangmin Xu & Xuehui Cui, 2018. "An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 69(1), pages 77-97, January.
    2. Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
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