The aim of this text is to highlight recent advances of trust-region-based methods for nonlinear programming and to put them into perspective. An algorithmic framework provides a ground with the main ideas of these methods and the related notation. Specific approaches concerned with handling the trust-region subproblem are recalled, particularly for the large scale setting. Recent contributions encompassing the trust-region globalization technique for nonlinear programming are reviewed, including nonmonotone acceptance criteria for unconstrained minimization; the adaptive adjustment of the trust-region radius; the merging of the trust-region step into a line search scheme, and the usage of the trust-region elements within derivative-free optimization algorithms.
trust-region methods; global convergence; nonlinear programming
