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Journal of Optimization Theory and Applications

, Volume 154, Issue 3, pp 904–915 | Cite as

Convergence Rate of the Pham Dinh–Le Thi Algorithm for the Trust-Region Subproblem

  • Hoang Ngoc TuanEmail author
Article

Abstract

We obtain sufficient conditions for the linear convergence of the iterative sequences produced by the Pham Dinh–Le Thi algorithm for the trust-region subproblem. In addition, we give two examples to show that, if the sufficient conditions are not satisfied, then the sequences may not be linearly convergent.

Keywords

Trust-region subproblem KKT point Lagrange multiplier DCA sequence Convergence rate 

Notes

Acknowledgements

This research was supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam. The author would like to thank Professor Nguyen Dong Yen for fruitful discussions on the topic, the two anonymous referees, and Professor Masao Fukushima for valuable comments, which have helped to improve greatly the presentation.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsHanoi Pedagogical University No. 2Phuc YenVietnam

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