期刊
OPTIMIZATION METHODS & SOFTWARE
卷 31, 期 5, 页码 1008-1035出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10556788.2016.1155213
关键词
unconstrained optimization; cubic regularization; Goldstein's line search; nonmonotone globalization methods; global convergence; 49M37; 65K05; 90C30
In recent years, cubic regularization algorithms for unconstrained optimization have been defined as alternatives to trust-region and line search schemes. These regularization techniques are based on the strategy of computing an (approximate) global minimizer of a cubic overestimator of the objective function. In this work we focus on the adaptive regularization algorithm using cubics (ARC) proposed in Cartis etal. [Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results, Mathematical Programming A 127 (2011), pp. 245-295]. Our purpose is to design a modified version of ARC in order to improve the computational efficiency preserving global convergence properties. The basic idea is to suitably combine a Goldstein-type line search and a nonmonotone accepting criterion with the aim of advantageously exploiting the possible good descent properties of the trial step computed as (approximate) minimizer of the cubic model. Global convergence properties of the proposed nonmonotone ARC algorithm are proved. Numerical experiments are performed and the obtained results clearly show satisfactory performance of the new algorithm when compared to the basic ARC algorithm.
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