Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(2): 589-600

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.589

Copyright © The Korean Mathematical Society.

A memory efficient incremental gradient method for regularized minimization

Sangwoon Yun

Sungkyunkwan University

Abstract

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of $m$ smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need $O(mn)$ storage, where $n$ is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only $O(n)$ storage.

Keywords: incremental gradient method, nonsmooth, regularization, running average

MSC numbers: Primary 49M27, 49M37, 65K05, 90C25, 90C30