Accelerated regularized Newton methods for minimizing composite convex functions

Geovani, Grapiglia () and Yurii, Nesterov ()
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Geovani, Grapiglia: Universidade Federal do Parana, Brazil
Yurii, Nesterov: CORE, Université catholique de Louvain

No 2018010, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, we study accelerated Regularized Newton Methods for minimizing objectives formed as a sum of two functions: one is convex and twice differentiable with Hölder-continuous Hessian, and the other is a simple closed convex function. For the case in which the Hölder parameter $\nu \in [0,1]$ is known, we propose methods that make at most $\cal {O}\left(\frac {1} {\epsilon^{1/(2+\nu)}}\right)$ iterations to reduce the funcitonal residual below a given precision $\epsilon > 0$. For the general case, in which the $\nu$ is not known, we proposeo a universal method that ensures the same precision in at most $\cal{O} \left(\frac {1} {\epsilon^{2/[3(1+\nu)]}}\right)$ iterations.

Keywords: unconstrianed minimizaiton; second-order methods; Hölder condition; worst-case global complexity bounds (search for similar items in EconPapers)
Date: 2018-03-23
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2018010

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