Behavior of DCA sequences for solving the trust‐region subproblem

From our results it follows that any DCA sequence for solving the trust‐region subproblem (Dinh and Thi, 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.