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Nonmonotone adaptive trust region method

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  • Shi, Zhenjun
  • Wang, Shengquan

Abstract

In this paper, we propose a nonmonotone adaptive trust region method for unconstrained optimization problems. This method can produce an adaptive trust region radius automatically at each iteration and allow the functional value of iterates to increase within finite iterations and finally decrease after such finite iterations. This nonmonotone approach and adaptive trust region radius can reduce the number of solving trust region subproblems when reaching the same precision. The global convergence and convergence rate of this method are analyzed under some mild conditions. Numerical results show that the proposed method is effective in practical computation.

Suggested Citation

  • Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:1:p:28-36
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    References listed on IDEAS

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    2. Z. J. Shi & J. Shen, 2005. "New Inexact Line Search Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 425-446, November.
    3. C. X. Xu & J. Z. Zhang, 1999. "Scaled Optimal Path Trust-Region Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 127-146, July.
    4. Bierlaire, M. & Thémans, M., 2009. "Dealing with singularities in nonlinear unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 196(1), pages 33-42, July.
    5. Polyak, B.T., 2007. "Newton's method and its use in optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1086-1096, September.
    6. Andrei, Neculai, 2010. "Accelerated scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 410-420, August.
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    Cited by:

    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. Zhou Sheng & Gonglin Yuan, 2018. "An effective adaptive trust region algorithm for nonsmooth minimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 251-271, September.
    3. Qu, Shaojian & Ji, Ying & Jiang, Jianlin & Zhang, Qingpu, 2017. "Nonmonotone gradient methods for vector optimization with a portfolio optimization application," European Journal of Operational Research, Elsevier, vol. 263(2), pages 356-366.

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