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A New Restarting Adaptive Trust-Region Method for Unconstrained Optimization

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Abstract

In this paper, we present a new adaptive trust-region method for solving nonlinear unconstrained optimization problems. More precisely, a trust-region radius based on a nonmonotone technique uses an approximation of Hessian which is adaptively chosen. We produce a suitable trust-region radius; preserve the global convergence under classical assumptions to the first-order critical points; improve the practical performance of the new algorithm compared to other exiting variants. Moreover, the quadratic convergence rate is established under suitable conditions. Computational results on the CUTEst test collection of unconstrained problems are presented to show the effectiveness of the proposed algorithm compared with some exiting methods.

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Authors and Affiliations

  1. Department of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran

    Morteza Kimiaei

  2. Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran

    Susan Ghaderi

Authors
  1. Morteza Kimiaei
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  2. Susan Ghaderi
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Correspondence to Morteza Kimiaei.

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Kimiaei, M., Ghaderi, S. A New Restarting Adaptive Trust-Region Method for Unconstrained Optimization. J. Oper. Res. Soc. China 5, 487–507 (2017). https://doi.org/10.1007/s40305-016-0149-8

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  • DOI: https://doi.org/10.1007/s40305-016-0149-8

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