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A dwindling filter line search method for unconstrained optimization


Authors: Yannan Chen and Wenyu Sun
Journal: Math. Comp. 84 (2015), 187-208
MSC (2010): Primary 65K05, 90C30
DOI: https://doi.org/10.1090/S0025-5718-2014-02847-0
Published electronically: May 19, 2014
MathSciNet review: 3266957
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Abstract: A dwindling multidimensional filter is proposed and applied to a second-order line search framework for unconstrained optimization. Usually, the multidimensional filter is built up with a fixed envelope, which is not well-suited to line search frameworks. In this paper, we propose the dwindling multidimensional filter, whose envelope is dwindling as the step-length of line search decreasing. Combining the dwindling multidimensional filter and a second-order line search, the new algorithm globally converges to a second-order critical point, when the negative curvature direction is exploited. Detailed numerical results on small and large CUTE test problems indicate that the new algorithm is more competitive than some classical line search methods.


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Yannan Chen
Affiliation: School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China; and School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Email: ynchen@zzu.edu.cn

Wenyu Sun
Affiliation: Corresponding author: School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China
Email: wysun@njnu.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-2014-02847-0
Keywords: Filter method, line search, negative curvature direction, unconstrained optimization, global convergence
Received by editor(s): January 12, 2011
Received by editor(s) in revised form: December 25, 2012, and May 1, 2013
Published electronically: May 19, 2014
Additional Notes: This work was supported by the National Natural Science Foundation of China (Nos. 11171159 and 11071122), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20103207110002), and the Graduate Student Research and Innovation Project of Jiangsu Province of China (No. CXZZ12_0384).
Article copyright: © Copyright 2014 American Mathematical Society