Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes

Nicola Bastianello; Andrea Simonetto; Ruggero Carli

doi:10.1109/ICASSP.2019.8682267

Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes

Nicola Bastianello, Andrea Simonetto, Ruggero Carli

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

Abstract

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm.

Original language	English
Title of host publication	2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5581-5585
Number of pages	5
ISBN (Electronic)	9781479981311
DOIs	https://doi.org/10.1109/ICASSP.2019.8682267
Publication status	Published - 1 May 2019
Externally published	Yes
Event	44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom Duration: 12 May 2019 → 17 May 2019

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2019-May
ISSN (Print)	1520-6149

Conference

Conference	44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Country/Territory	United Kingdom
City	Brighton
Period	12/05/19 → 17/05/19

Keywords

convex optimization
forward-backward envelope
prediction-correction methods
time-varying optimization

Access to Document

10.1109/ICASSP.2019.8682267

Cite this

Bastianello, N., Simonetto, A., & Carli, R. (2019). Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings (pp. 5581-5585). Article 8682267 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2019.8682267

Bastianello, Nicola ; Simonetto, Andrea ; Carli, Ruggero. / Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes. 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 5581-5585 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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title = "Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes",

abstract = "We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm.",

keywords = "convex optimization, forward-backward envelope, prediction-correction methods, time-varying optimization",

author = "Nicola Bastianello and Andrea Simonetto and Ruggero Carli",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 ; Conference date: 12-05-2019 Through 17-05-2019",

year = "2019",

month = may,

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doi = "10.1109/ICASSP.2019.8682267",

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series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

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Bastianello, N, Simonetto, A & Carli, R 2019, Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes. in 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings., 8682267, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2019-May, Institute of Electrical and Electronics Engineers Inc., pp. 5581-5585, 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019, Brighton, United Kingdom, 12/05/19. https://doi.org/10.1109/ICASSP.2019.8682267

Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes. / Bastianello, Nicola; Simonetto, Andrea; Carli, Ruggero.
2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 5581-5585 8682267 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May).

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

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N2 - We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm.

AB - We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward envelope, and we are able to prove the convergence of the solutions to a neighborhood of the optimizer that depends on the sampling time. Numerical simulations for a time-varying regression problem with elastic net regularization highlight the effectiveness of the algorithm.

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KW - forward-backward envelope

KW - prediction-correction methods

KW - time-varying optimization

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DO - 10.1109/ICASSP.2019.8682267

M3 - Conference contribution

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Bastianello N, Simonetto A, Carli R. Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 5581-5585. 8682267. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2019.8682267

Prediction-correction for Nonsmooth Time-varying Optimization via Forward-backward Envelopes

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