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Convergence rate of a penalty method for strongly convex problems with linear constraints

Nedić, Angelia ; Tatarenko, Tatiana (2025)
Convergence rate of a penalty method for strongly convex problems with linear constraints.
59th IEEE Conference on Decision and Control (CDC 2020). Jeju, Südkorea (14.12.2020-18.12.2020)
doi: 10.26083/tuprints-00017869
Conference or Workshop Item, Secondary publication, Postprint

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Item Type: Conference or Workshop Item
Type of entry: Secondary publication
Title: Convergence rate of a penalty method for strongly convex problems with linear constraints
Language: English
Date: 20 January 2025
Place of Publication: Darmstadt
Year of primary publication: 14 December 2020
Place of primary publication: New York, NY
Publisher: IEEE
Book Title: 2020 59th IEEE Conference on Decision and Control (CDC 2020)
Collation: 6 Seiten
Event Title: 59th IEEE Conference on Decision and Control (CDC 2020)
Event Location: Jeju, Südkorea
Event Dates: 14.12.2020-18.12.2020
DOI: 10.26083/tuprints-00017869
Corresponding Links:
Origin: Secondary publication service
Abstract:

We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a version of the one-sided Huber losses. The smoothness properties of these functions allow us to choose time-varying penalty parameters in such a way that the incremental procedure with the diminishing step-size converges √ to the exact solution with the rate O(1/√k). To the best of our knowledge, we present the first result on the convergence rate for the penalty-based gradient method, in which the penalty parameters vary with time.

Status: Postprint
URN: urn:nbn:de:tuda-tuprints-178698
Classification DDC: 500 Science and mathematics > 500 Science
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik
18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Robotics (from 01.08.2022 renamed Control Methods and Intelligent Systems)
Date Deposited: 20 Jan 2025 10:50
Last Modified: 20 Jan 2025 10:50
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/17869
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