A Globally Convergent Trust-Region Algorithm for Unconstrained Optimization Using Filter

We introduce a new filter acceptance criterion for unconstrained optimization. Using this criterion, we present a new filter trust-region algorithm for solving unconstrained nonlinear optimization problems. The new criterion has the property that guarantees the finiteness of the filter size. We also show a correlation between problem dimension and filter size. We then show that at least one of the limit points of the sequence of the iterates is firstorder critical, and strengthen the result by showing the first order criticality of all the limit points of the sequence of the iterates for a modified version of the algorithm. Finally, we compare our algorithm with some other existing filter trust-region algorithms on the collection of CUTEr unconstrained test problems.