Open AccessA dual Bregman proximal gradient method for relatively-strongly convex optimization
Author(s) -
Jin-Zan Liu,
Xinwei Li
Publication year - 2022
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2021028
Subject(s) - mathematics , combinatorics , regular polygon , convex function , sequence (biology) , function (biology) , bregman divergence , convex optimization , geometry , genetics , evolutionary biology , biology
We consider a convex composite minimization problem, whose objective is the sum of a relatively-strongly convex function and a closed proper convex function. A dual Bregman proximal gradient method is proposed for solving this problem and is shown that the convergence rate of the primal sequence is \begin{document}$ O(\frac{1}{k}) $\end{document} . Moreover, based on the acceleration scheme, we prove that the convergence rate of the primal sequence is \begin{document}$ O(\frac{1}{k^{\gamma}}) $\end{document} , where \begin{document}$ \gamma\in[1,2] $\end{document} is determined by the triangle scaling property of the Bregman distance.