On the Exponential Stability of Primal-Dual Gradient Dynamics

Continuous time primal-dual gradient dynamics (PDGD) that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it is less studied whether they are globally exponentia...

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Published inIEEE control systems letters Vol. 3; no. 1; pp. 43 - 48
Main Authors Qu, Guannan, Li, Na
Format Journal Article
LanguageEnglish
Published IEEE 01.01.2019
Subjects
Asymptotic stability
Control theory
Convergence
Lyapunov methods
Optimization
Power system dynamics
Stability
stability of nonlinear systems
Symmetric matrices
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Abstract Continuous time primal-dual gradient dynamics (PDGD) that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it is less studied whether they are globally exponentially stable. In this letter, we study the PDGD for convex optimization with strongly convex and smooth objectives and affine equality or inequality constraints, and prove global exponential stability for such dynamics. Bounds on decaying rates are provided.
AbstractList Continuous time primal-dual gradient dynamics (PDGD) that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it is less studied whether they are globally exponentially stable. In this letter, we study the PDGD for convex optimization with strongly convex and smooth objectives and affine equality or inequality constraints, and prove global exponential stability for such dynamics. Bounds on decaying rates are provided.
Author Na Li
Guannan Qu
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Snippet Continuous time primal-dual gradient dynamics (PDGD) that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and...
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Publisher
StartPage 43
SubjectTerms Asymptotic stability
Control theory
Convergence
Lyapunov methods
Optimization
Power system dynamics
Stability
stability of nonlinear systems
Symmetric matrices
Title On the Exponential Stability of Primal-Dual Gradient Dynamics
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