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Hybridizing monotone and nonmonotone approaches, we employ a modified trust region ratio in which more information is provided about the agreement between the exact and the approximate models. Also, we use an adaptive trust region radius as well as two accelerated Armijo-type line search strategies to avoid resolving the trust region subproblem whenever a trial step is rejected. We show that the proposed algorithm is globally and locally superlinearly convergent. Comparative numerical experiments show practical efficiency of the proposed accelerated adaptive trust region algorithm. [ABSTRACT FROM AUTHOR]

We present a new smaller upper bound for all the elements in the associate generalized Hessian used in the smoothing quadratic regularization (SQR) algorithm proposed by Bian and Chen (SIAM J. Optim. 23: 1718-1741, ). We modify the SQR algorithm by making use of the new upper bound. Numerical results show that our new upper bound improves the performance of the SQR algorithm significantly. [ABSTRACT FROM AUTHOR]