Stability of primal–dual gradient dynamics and applications to network optimization

2010/09/02 by Diego Feijer, Fernando Paganini · 352 citations
Computer Science · Mathematics · #Computer science #Convex function #Distributed Control Multi-Agent Systems #Dual (grammatical number) #Invariance principle #Lyapunov function #Mathematical optimization #Mathematical proof #Mathematics #Mobile Ad Hoc Networks #Network Traffic and Congestion Control #Optimization problem #Regular polygon #Saddle #Saddle point #Stability (learning theory)

paper · doi:10.1016/j.automatica.2010.08.011

published in Automatica 46(12), 1974-1981 (Elsevier BV)

openalex publication_date 2010/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Cited by

• Passivity-Based Distributed Optimization with Communication Delays Using PI Consensus Algorithm
• Distributed Automatic Load-Frequency Control with Optimality in Power Systems
• Aug-PDG: Linear Convergence of Convex Optimization with Inequality Constraints
• Krasovskii's Passivity
• Training Generative Adversarial Networks via Primal-Dual Subgradient Methods: A Lagrangian Perspective on GAN
• A unifying energy-based approach to optimal frequency and market regulation in power grids
• Small-Gain Nash: Certified Contraction to Nash Equilibria in Differentiable Games
• Acceleration of Primal-Dual Methods by Preconditioning and Simple Subproblem Procedures
• Online Learning of Feasible Strategies in Unknown Environments
• Stability Analysis of Constrained Optimization Dynamics via Passivity Techniques
• Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems
• Exponential Stability of Partial Primal-Dual Gradient Dynamics with Nonsmooth Objective Functions
• Distributed coordination for nonsmooth convex optimization via saddle-point dynamics
• A projection-free dynamics for nonsmooth composite optimization
• Composite Lyapunov Criteria for Stability and Convergence with Applications to Optimization Dynamics
• Optimization via a Control-Centric Framework
• Distributed linear programming with event-triggered communication
• An Optimal Control Interpretation of Augmented Distributed Optimization Algorithms
• On the Exponential Stability of Projected Primal-Dual Dynamics on a Riemannian Manifold
• Network coding for multicasting over Rayleigh fading multi access channels
• HVAC system dynamic management in communities via an aggregation–disaggregation framework
• Alternative passive maps in the Brayton-Moser framework: Implications on control and optimization
• Equilibrium-Independent Dissipativity with Quadratic Supply Rates
• Hybrid Voltage Control in Distribution Networks Under Limited Communication Rates
• Primal-Dual Gradient Flow Algorithm for Distributed Support Vector Machines
• REAP-T: A MATLAB Toolbox for Implementing Robust-to-Early Termination Model Predictive Control
• Distributed and time-varying primal-dual dynamics via contraction analysis
• Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian: A Lyapunov-based approach
• Preconditioned primal-dual dynamics in convex optimization: non-ergodic convergence rates
• Bias estimation in sensor networks
• On the primal-dual dynamics of Support Vector Machines
• Primal-Dual Sequential Subspace Optimization for Saddle-point Problems
• On the Geometry and Linear Convergence of Primal-Dual Dynamics
• Distributed continuous-time convex optimization on weight-balanced\n digraphs