TY - JOUR
T1 - Stochastic Trust-Region Methods with Trust-Region Radius Depending on Probabilistic Models
AU - Wang , Xiaoyu
AU - Yuan , Yaxiang
JO - Journal of Computational Mathematics
VL - 2
SP - 294
EP - 334
PY - 2022
DA - 2022/01
SN - 40
DO - http://doi.org/10.4208/jcm.2012-m2020-0144
UR - https://global-sci.org/intro/article_detail/jcm/20188.html
KW - Trust-region methods, Stochastic optimization, Probabilistic models, Trust-region radius, Global convergence.
AB - <p style="text-align: justify;">We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm termed STRME, in which the trust-region radius depends linearly on the gradient used to define the latest model. The complexity results of the STRME method in nonconvex, convex and strongly convex settings are presented, which match those of the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.</p>