Numerical Experience with a Class of Trust-Region Algorithms for Unconstrained Smooth Optimization

In this paper we investigate the numerical performance of trust-region algorithms in which the trust-region radius is updated by a nonlinear rule according with the quality of the models. This class of algorithms fits into the Nonlinear Stepsize Control framework recently proposed by Toint (Optimization Methods and Software 28: 82–95, 2013). The nonlinear control of the trust-region radius is characterized by a pair (α,β ) of user-defined parameters. Notable particular cases are the standard trust-region algorithm and the Fan-Yuan trust-region algorithm, which are obtained, respectively, with the traditional choices (α,β ) = (1,0) and (α,β ) = (1,1). As expected, our numerical results show that the numerical behaviour in this class of trust-region algorithms can vary greatly with different choices for (α,β ). In particular, we have identified pairs of parameters which are more efficient than the traditional ones.