Behavior of DCA sequences for solving the trust-region subproblem

摘要

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.