Concise Complexity Analyses for Trust-Region Methods

Frank E. Curtis (frank.e.curtisgmail.com)
Zachary Lubberts (zlubber1jhu.edu)
Daniel P. Robinson (daniel.p.robinsongmail.com)

Abstract: 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.

Keywords: unconstrained optimization, nonlinear optimization, nonconvex optimization, trust region methods, global convergence, worst-case iteration complexity, worst-case evaluation complexity

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: F. E. Curtis, Z. Lubberts, and D. P. Robinson. Concise Complexity Analyses for Trust Region Methods. Optimization Letters, 12(8):1713–1724, 2018.

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Entry Submitted: 02/21/2018
Entry Accepted: 02/21/2018
Entry Last Modified: 08/26/2019

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