Accelerated Gradient Descent Method for Projections onto the ℓ1-Ball

Paul Rodriguez

doi:10.1109/IVMSPW.2018.8448778

Accelerated Gradient Descent Method for Projections onto the ℓ₁-Ball

Paul Rodriguez

Sección de Electricidad y Electrónica

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

We present a computationally efficient algorithm to solve the projection onto the ℓ₁-ball problem, which is cast as an equivalent univariate optimization problem by means of its dual formulation, the ℓ_∞ proximity operator. Our algorithm, which is a customization of the Nesterov's accelerated gradient descent method, is empirically demonstrated to be faster than the state-of-the-art methods for the projection onto the ℓ₁-ball problem.

Original language	English
Title of host publication	2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Print)	9781538609514
DOIs	https://doi.org/10.1109/IVMSPW.2018.8448778
State	Published - 27 Aug 2018
Event	13th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Zagori, Greece Duration: 10 Jun 2018 → 12 Jun 2018

Publication series

Name	2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings

Conference

Conference	13th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018
Country/Territory	Greece
City	Zagori
Period	10/06/18 → 12/06/18

Keywords

Accelerated gradient descent
Projection onto the ball
proximity operator

Access to Document

10.1109/IVMSPW.2018.8448778

Cite this

Rodriguez, P. (2018). Accelerated Gradient Descent Method for Projections onto the ℓ₁-Ball. In 2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings Article 8448778 (2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IVMSPW.2018.8448778

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abstract = "We present a computationally efficient algorithm to solve the projection onto the ℓ1-ball problem, which is cast as an equivalent univariate optimization problem by means of its dual formulation, the ℓ∞ proximity operator. Our algorithm, which is a customization of the Nesterov's accelerated gradient descent method, is empirically demonstrated to be faster than the state-of-the-art methods for the projection onto the ℓ1-ball problem.",

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note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 13th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 ; Conference date: 10-06-2018 Through 12-06-2018",

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Rodriguez, P 2018, Accelerated Gradient Descent Method for Projections onto the ℓ₁-Ball. in 2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings., 8448778, 2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings, Institute of Electrical and Electronics Engineers Inc., 13th IEEE Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018, Zagori, Greece, 10/06/18. https://doi.org/10.1109/IVMSPW.2018.8448778

Accelerated Gradient Descent Method for Projections onto the ℓ₁-Ball. / Rodriguez, Paul.
2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. 8448778 (2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We present a computationally efficient algorithm to solve the projection onto the ℓ1-ball problem, which is cast as an equivalent univariate optimization problem by means of its dual formulation, the ℓ∞ proximity operator. Our algorithm, which is a customization of the Nesterov's accelerated gradient descent method, is empirically demonstrated to be faster than the state-of-the-art methods for the projection onto the ℓ1-ball problem.

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Rodriguez P. Accelerated Gradient Descent Method for Projections onto the ℓ₁-Ball. In 2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2018. 8448778. (2018 IEEE 13th Image, Video, and Multidimensional Signal Processing Workshop, IVMSP 2018 - Proceedings). doi: 10.1109/IVMSPW.2018.8448778