Journal of Global Optimization

, Volume 53, Issue 2, pp 317–329 | Cite as

Behavior of DCA sequences for solving the trust-region subproblem

  • Hoai An Le ThiEmail author
  • Tao Pham Dinh
  • Nguyen Dong Yen


From our results it follows that any DCA sequence for solving the trust-region subproblem (see Pham Dinh and Le Thi, in SIAM J Optim 8:476–505, 1998) is convergent provided that the basic matrix of the problem is nonsingular and it does not have multiple negative eigenvalues. Besides, under this additional assumption, there exists such an open set Ω containing the global minimizers and the unique local-nonglobal minimizer (if such exists) that any DCA sequence with the initial point from Ω is contained in the set and converges to a global minimizer or the local-nonglobal minimizer. Various examples are given to illustrate the limiting behavior and stability of the DCA sequences. Structure of the KKT point set of the trust-region subproblem is also analyzed.


Trust-region subproblem DC algorithm DCA sequence Limiting behavior and stability Multiplicity of nonpositive eigenvalue 

Mathematics Subject Classification (2000)

65K05 65K10 90C30 90C35 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Hoai An Le Thi
    • 1
    Email author
  • Tao Pham Dinh
    • 2
  • Nguyen Dong Yen
    • 3
  1. 1.Laboratory of Theoretical and Applied Computer Science (LITA)Paul Verlaine University of MetzMetz CedexFrance
  2. 2.Laboratory of Modelling, Optimization and Operations Research (LMI)National Institute for Applied Sciences (INSA) - RouenSaint-Etienne-du-RouvrayFrance
  3. 3.Vietnamese Academy of Science and TechnologyInstitute of MathematicsHanoiVietnam

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