Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain control over the choice of trust region radius after any successful iteration. The analyses highlight the essential algorithm components required to obtain certain complexity bounds. In addition, a new update strategy for the trust region radius is proposed that offers a second-order complexity bound.
F. E. Curtis, Z. Lubberts, and D. P. Robinson. Concise Complexity Analyses for Trust Region Methods. Optimization Letters, 12(8):1713–1724, 2018.