scholarly journals Decentralized Accelerated Gradient Methods With Increasing Penalty Parameters

2020 ◽  
Vol 68 ◽  
pp. 4855-4870
Author(s):  
Huan Li ◽  
Cong Fang ◽  
Wotao Yin ◽  
Zhouchen Lin
Keyword(s):  
Gradient Methods ◽  
Accelerated Gradient ◽  
Accelerated Gradient Methods

scholarly journals Adaptive restart of accelerated gradient methods under local quadratic growth condition

2019 ◽  
Vol 39 (4) ◽  
pp. 2069-2095 ◽  
Author(s):  
Olivier Fercoq ◽  
Zheng Qu
Keyword(s):  
Growth Condition ◽  
Error Bound ◽  
Gradient Methods ◽  
Quadratic Growth ◽  
Quadratic Error ◽  
Total Variation Denoising ◽  
Accelerated Gradient ◽  
Convergent Algorithm ◽  
Accelerated Gradient Methods ◽  
Quadratic Growth Condition

Abstract By analyzing accelerated proximal gradient methods under a local quadratic growth condition, we show that restarting these algorithms at any frequency gives a globally linearly convergent algorithm. This result was previously known only for long enough frequencies. Then as the rate of convergence depends on the match between the frequency and the quadratic error bound, we design a scheme to automatically adapt the frequency of restart from the observed decrease of the norm of the gradient mapping. Our algorithm has a better theoretical bound than previously proposed methods for the adaptation to the quadratic error bound of the objective. We illustrate the efficiency of the algorithm on Lasso, regularized logistic regression and total variation denoising problems.

scholarly journals Robust Accelerated Gradient Methods for Smooth Strongly Convex Functions

2020 ◽  
Vol 30 (1) ◽  
pp. 717-751
Author(s):  
Necdet Serhat Aybat ◽  
Alireza Fallah ◽  
Mert Gürbüzbalaban ◽  
Asuman Ozdaglar
Keyword(s):  
Convex Functions ◽  
Gradient Methods ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Accelerated Gradient ◽  
Accelerated Gradient Methods
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