基于最优解距离估计的光滑凸极小化的一阶算法

doi:10.6040/j.issn.1671-9352.0.2019.815

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (4): 102-107.doi: 10.6040/j.issn.1671-9352.0.2019.815

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基于最优解距离估计的光滑凸极小化的一阶算法

陈倩竹,胡海平^*

上海大学理学院, 上海 200444

发布日期:2020-04-09
作者简介:陈倩竹(1994— ),女,硕士研究生,研究方向为图像处理与模式识别. E-mail:qianzhuchen@i.shu.edu.cn*通信作者简介:胡海平(1966— ),男,副教授,研究方向为图像处理与模式识别. E-mail:hu_jack@staff.shu.edu.cn

Optimizing the efficiency of first-order methods for the distance to an optimal solution of smooth convex functions

CHEN Qian-zhu, HU Hai-ping^*

School of Science, Shanghai University, Shanghai 200444, China

Published:2020-04-09

摘要/Abstract

摘要： 利用性能估计问题(PEP)方法,通过研究最优解距离‖x_N-x_*‖2的最坏情况性能,对光滑凸极小化的一阶方法的步长系数进行了优化,使其收敛速度达到O(1/N 2)。

关键词: 一阶方法, 光滑凸极小化, 最坏情况性能分析, 收敛速度

Abstract: We use the performance estimation problem(PEP)method to optimize the step coefficient of the first-order smooth convex minimization method by studying the worst-case estimation of the optimal solution distance ‖x_N-x_*‖2, and the convergence rate can reach O(1/N 2).

Key words: first-order method, smooth convex minimization, worst-case performance analysis, rate of convergence

中图分类号:

O224

陈倩竹,胡海平. 基于最优解距离估计的光滑凸极小化的一阶算法[J]. 《山东大学学报(理学版)》, 2020, 55(4): 102-107.

CHEN Qian-zhu, HU Hai-ping. Optimizing the efficiency of first-order methods for the distance to an optimal solution of smooth convex functions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 102-107.

参考文献

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[3] DRORI Y,TEBOULLE M. Performance of first-order methods for smooth convex minimization: a novel approach[J]. Mathematical Programming, 2014, 145(1/2):451-482.
[4] KIM D, FESSLER J A. Optimized first-order methods for smooth convex minimization[J]. Mathematical Programming, 2016, 159(1/2):81-107.
[5] TAYLOR A B, HENDRICKX J M, GLINEUR F. Smooth strongly convex interpolation and exact worst-case performance of first-order methods[J]. Mathematical Programming, 2017, 161(1): 307-345.
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基于最优解距离估计的光滑凸极小化的一阶算法

Optimizing the efficiency of first-order methods for the distance to an optimal solution of smooth convex functions

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