Convergence of first-order methods via the convex conjugate

被引：4

作者：

Pena, Javier ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Tepper Sch Business, Pittsburgh, PA 15213 USA

来源：

OPERATIONS RESEARCH LETTERS | 2017年 / 45卷 / 06期

基金：

美国国家科学基金会;

关键词：

First-order methods; Conjugate; Acceleration; ALGORITHMS;

D O I：

10.1016/j.orl.2017.08.013

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper gives a unified and succinct approach to the O(1/root O, O(1/k), and O(1/k(2)) convergence rates of the subgradient, gradient, and accelerated gradient methods for unconstrained convex minimization. In the three cases the proof of convergence follows from a generic bound defined by the convex conjugate of the objective function. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：561 / 564

页数：4

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