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Concise complexity analyses for trust region methods

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Abstract

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain control over the choice of trust region radius after any successful iteration. The analyses highlight the essential algorithm components required to obtain certain complexity bounds. In addition, a new update strategy for the trust region radius is proposed that offers a second-order complexity bound.

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Notes

  1. http://web.stanford.edu/class/msande311/lecture13.pdf.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA

    Frank E. Curtis

  2. Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA

    Zachary Lubberts & Daniel P. Robinson

Authors
  1. Frank E. Curtis
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  2. Zachary Lubberts
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  3. Daniel P. Robinson
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Correspondence to Daniel P. Robinson.

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Curtis, F.E., Lubberts, Z. & Robinson, D.P. Concise complexity analyses for trust region methods. Optim Lett 12, 1713–1724 (2018). https://doi.org/10.1007/s11590-018-1286-2

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  • DOI: https://doi.org/10.1007/s11590-018-1286-2

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