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

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" TargetType="DOI"/> , 2010).