Summary: A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by R. Flechter
and S. Leyffer
[Math. Program. 91, No. 2 (A), 239–269 (2002; Zbl 1049.90088
)], it extends an existing technique of N. I. M. Gould, S. Leyffer
and P. Toint
[SIAM J. Optim. 15, No. 1, 17-38 (2004; Zbl 1075.65075
)] for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algorithm is shown to be globally convergent to at least one second-order critical point, and numerical experiments indicate that it is very competitive with more classical trust-region algorithms.