A Retrospective Trust Region Algorithm with Trust Region Converging to Zero

Authors

  • Jinyan Fan School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
  • Jianyu Pan Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China
  • Hongyan Song School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

DOI:

https://doi.org/10.4208/jcm.1601-m2015-0399

Keywords:

Retrospective trust region algorithm, Unconstrained optimization, Superlinear convergence.

Abstract

We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algorithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.

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Published

2018-08-22

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Issue

Vol. 34 No. 4 (2016)

Section

Articles

How to Cite

A Retrospective Trust Region Algorithm with Trust Region Converging to Zero. (2018). Journal of Computational Mathematics, 34(4), 421-436. https://doi.org/10.4208/jcm.1601-m2015-0399