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Volume 40, Issue 2
Stochastic Trust-Region Methods with Trust-Region Radius Depending on Probabilistic Models

Xiaoyu Wang & Yaxiang Yuan

J. Comp. Math., 40 (2022), pp. 294-334.

Published online: 2022-01

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  • Abstract

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.

  • Keywords

Trust-region methods, Stochastic optimization, Probabilistic models, Trust-region radius, Global convergence.

  • AMS Subject Headings

65K05, 65K10, 90C60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wxy@lsec.cc.ac.cn (Xiaoyu Wang)

yyx@lsec.cc.ac.cn (Yaxiang Yuan)

  • BibTex
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@Article{JCM-40-294, author = {Xiaoyu and Wang and wxy@lsec.cc.ac.cn and 22002 and Institute of Computational Mathematics and Scienti c/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and Xiaoyu Wang and Yaxiang and Yuan and yyx@lsec.cc.ac.cn and 13421 and LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and Yaxiang Yuan}, title = {Stochastic Trust-Region Methods with Trust-Region Radius Depending on Probabilistic Models}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {2}, pages = {294--334}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2012-m2020-0144}, url = {http://global-sci.org/intro/article_detail/jcm/20188.html} }
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.

Xiaoyu Wang & Yaxiang Yuan. (2022). Stochastic Trust-Region Methods with Trust-Region Radius Depending on Probabilistic Models. Journal of Computational Mathematics. 40 (2). 294-334. doi:10.4208/jcm.2012-m2020-0144
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