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Convergence of Pham Dinh–Le Thi’s algorithm for the trust-region subproblem

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Abstract

It is proved that any DCA sequence constructed by Pham Dinh–Le Thi’s algorithm for the trust-region subproblem (Pham Dinh and Le Thi, in SIAM J. Optim. 8:476–505, 1998) converges to a Karush–Kuhn–Tucker point of the problem. This result provides a complete solution for one open question raised by Le Thi et al. (J. Global Optim., Online First, doi:10.1007/s10898-011-9696-z, 2010).

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Authors and Affiliations

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

    Hoang Ngoc Tuan

  2. Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Nguyen Dong Yen

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  1. Hoang Ngoc Tuan
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  2. Nguyen Dong Yen
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Correspondence to Nguyen Dong Yen.

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Tuan, H.N., Yen, N.D. Convergence of Pham Dinh–Le Thi’s algorithm for the trust-region subproblem. J Glob Optim 55, 337–347 (2013). https://doi.org/10.1007/s10898-011-9820-0

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  • DOI: https://doi.org/10.1007/s10898-011-9820-0

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