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...</citationref>

In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the application of trust-region methods to the solution of a class of nonlinear optimization problems where the constrained set is closed and convex (and, from a practical point of view, where...

We obtain necessary and sufficient conditions for local Lipschitz-like property and sufficient conditions for local metric regularity in Robinson’s sense of Karush–Kuhn–Tucker point set maps of trust-region subproblems in trust-region methods. The main tools being used in our investigation...

Based on the NEWUOA algorithm, a new derivative-free algorithm is developed, named LCOBYQA. The main aim of the algorithm is to find a minimizer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$x^{*} \in\mathbb{R}^{n}$</EquationSource> </InlineEquation> of a non-linear function, whose derivatives are unavailable, subject to linear inequality constraints. The algorithm is...</equationsource></inlineequation>