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

摘要

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/sl0898-011-9696-z, 2010).