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

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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.

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References

  1. Conn, A.R., Gould, N.I.M., Toint, P.L.: In: Trust-Region Methods. MPS-SIAM Series on Optimization. SIAM, Philadelphia (2000)

    Chapter  Google Scholar 

  2. Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to D.C. programming: theory, algorithms and applications. Acta Math. Vietnam. 22, 289–355 (1997)

    MathSciNet  MATH  Google Scholar 

  3. Pham Dinh, T., Le Thi, H.A.: A D.C. optimization algorithm for solving the trust-region subproblem. SIAM J. Optim. 8, 476–505 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Le Thi, H.A., Pham Dinh, T., Yen, N.D.: Behavior of DCA sequences for solving the trust-region subproblem. J. Glob. Optim. (2010). Online First. doi:10.1007/s10898-011-9696-z

    Google Scholar 

  5. Tuan, H.N., Yen, N.D.: Convergence of Pham Dinh–Le Thi algorithm for the trust-region subproblem. J. Glob. Optim. (2011). Online First. doi:10.1007/s10898-011-9820-0

    Google Scholar 

  6. Martinez, J.M.: Local minimizers of quadratic functions on Euclidean balls and spheres. SIAM J. Optim. 4, 159–176 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pham Dinh, T., Le Thi, H.A.: Lagrangian stability and global optimality on nonconvex quadratic minimization over Euclidean balls and spheres. J. Convex Anal. 2, 263–276 (1995)

    MathSciNet  MATH  Google Scholar 

  8. Pardalos, P.M., Resende, M.G.C.: Handbook of Applied Optimization. Oxford University Press, New York (2002)

    MATH  Google Scholar 

  9. Stoer, J., Burlish, R.: Introduction to Numerical Analysis, 3rd edn. Springer, New York (2002)

    MATH  Google Scholar 

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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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Authors and Affiliations

  1. Department of Mathematics, Hanoi Pedagogical University No. 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    Hoang Ngoc Tuan

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  1. Hoang Ngoc Tuan
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Correspondence to Hoang Ngoc Tuan.

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Communicated by Masao Fukushima.

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Ngoc Tuan, H. Convergence Rate of the Pham Dinh–Le Thi Algorithm for the Trust-Region Subproblem. J Optim Theory Appl 154, 904–915 (2012). https://doi.org/10.1007/s10957-012-0041-6

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  • DOI: https://doi.org/10.1007/s10957-012-0041-6

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