Journal of Global Optimization

, Volume 55, Issue 2, pp 337–347 | Cite as

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

  • Hoang Ngoc Tuan
  • Nguyen Dong YenEmail author


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).


Trust-region subproblem d.c. Algorithm DCA sequence Convergence KKT point 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of MathematicsHanoi Pedagogical Institute No. 2Phuc YenVietnam
  2. 2.Institute of MathematicsVietnamese Academy of Science and TechnologyHanoiVietnam

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