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, <CitationRef CitationID="CR13">1998</CitationRef>) 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:<ExternalRef> <RefSource>10.1007/s10898-011-9696-z</RefSource> <RefTarget Address="10.1007/s10898-011-9696-z" TargetType="DOI"/> </ExternalRef>, <CitationRef CitationID="CR7">2010</CitationRef>). Copyright Springer Science+Business Media, LLC. 2013