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 -

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.