scholarly journals Exact Linear Convergence Rate Analysis for Low-Rank Symmetric Matrix Completion via Gradient Descent

2021 ◽  
Author(s):  
Trung Vu ◽  
Raviv Raich
Keyword(s):  
Convergence Rate ◽  
Gradient Descent ◽  
Symmetric Matrix ◽  
Matrix Completion ◽  
Linear Convergence ◽  
Low Rank ◽  
Linear Convergence Rate ◽  
Rate Analysis ◽  
Convergence Rate Analysis

A modified limited memory steepest descent method motivated by an inexact super-linear convergence rate analysis

2020 ◽  
Author(s):  
Ran Gu ◽  
Qiang Du
Keyword(s):  
Convergence Rate ◽  
Linear Convergence ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Step Size ◽  
Linear Convergence Rate ◽  
Limited Memory ◽  
Rate Analysis ◽  
Convergence Rate Analysis

Abstract How to choose the step size of gradient descent method has been a popular subject of research. In this paper we propose a modified limited memory steepest descent method (MLMSD). In each iteration we propose a selection rule to pick a unique step size from a candidate set, which is calculated by Fletcher’s limited memory steepest descent method (LMSD), instead of going through all the step sizes in a sweep, as in Fletcher’s original LMSD algorithm. MLMSD is motivated by an inexact super-linear convergence rate analysis. The R-linear convergence of MLMSD is proved for a strictly convex quadratic minimization problem. Numerical tests are presented to show that our algorithm is efficient and robust.

scholarly journals Surpassing Gradient Descent Provably: A Cyclic Incremental Method with Linear Convergence Rate

2018 ◽  
Vol 28 (2) ◽  
pp. 1420-1447 ◽  
Author(s):  
Aryan Mokhtari ◽  
Mert Gürbüzbalaban ◽  
Alejandro Ribeiro
Keyword(s):  
Convergence Rate ◽  
Gradient Descent ◽  
Linear Convergence ◽  
Linear Convergence Rate ◽  
Incremental Method

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

scholarly journals A Decentralized Second-Order Method with Exact Linear Convergence Rate for Consensus Optimization

2016 ◽  
Vol 2 (4) ◽  
pp. 507-522 ◽  
Author(s):  
Aryan Mokhtari ◽  
Wei Shi ◽  
Qing Ling ◽  
Alejandro Ribeiro
Keyword(s):  
Convergence Rate ◽  
Linear Convergence ◽  
Second Order ◽  
Order Method ◽  
Linear Convergence Rate ◽  
Consensus Optimization

Convergence rate analysis for the higher order power method in best rank one approximations of tensors

2018 ◽  
Vol 140 (4) ◽  
pp. 993-1031 ◽  
Author(s):  
Shenglong Hu ◽  
Guoyin Li
Keyword(s):  
Convergence Rate ◽  
Higher Order ◽  
Power Method ◽  
Rate Analysis ◽  
Rank One ◽  
Convergence Rate Analysis
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