  This paper addresses some trust-region methods equipped with nonmonotone
strategies for solving nonlinear unconstrained optimization problems. More
specifically, the importance of using nonmonotone techniques in nonlinear
optimization is motivated, then two new nonmonotone terms are proposed, and
their combinations into the traditional trust-region framework are studied. The
global convergence to first- and second-order stationary points and local
superlinear and quadratic convergence rates for both algorithms are
established. Numerical experiments on the \textsf{CUTEst} test collection of
unconstrained problems and some highly nonlinear test functions are reported,
where a comparison among state-of-the-art nonmonotone trust-region methods show
the efficiency of the proposed nonmonotne schemes.

Optimization and Control