Semiglobal exponential stability of the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm for constrained optimization
File(s)
Published version
Author(s)
Bin, Michelangelo
Notarnicola, Ivano
Parisini, Thomas
Type
Journal Article
Abstract
We consider the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm, also known as the first-order Lagrangian method, for constrained optimization problems involving a smooth strongly convex cost and smooth convex constraints. We prove that, for every given compact set of initial conditions, there always exists a sufficiently small stepsize guaranteeing exponential stability of the optimal primal-dual solution of the problem with a domain of attraction including the initialization set. Inspired by the analysis of nonlinear oscillators, the stability proof is based on a non-quadratic Lyapunov function including a nonlinear cross term.
Date Issued
2024-11-01
Date Acceptance
2023-12-16
Citation
Mathematical programming, 2024, 208 (1-2), pp.629-660
ISSN
0025-5610
Publisher
Springer
Start Page
629
End Page
660
Journal / Book Title
Mathematical programming
Volume
208
Issue
1-2
Copyright Statement
©TheAuthor(s) 2024 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Subjects
Computer Science
Computer Science, Software Engineering
Constraint programming
CONVERGENCE
Convex programming
Discrete-time control/observation systems
DISTRIBUTED OPTIMIZATION
DYNAMICS
Mathematics
Mathematics, Applied
Operations Research & Management Science
Physical Sciences
Primal-dual algorithm
Science & Technology
Technology
Publication Status
Published
Date Publish Online
2024-02-12