A PID feedback law on dual variables induces a unified family of saddle-point flows for constrained optimization, with explicit global exponential convergence guarantees under convexity and affine constraints.
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PI-PGD dynamics have equilibria equivalent to stationary points of equality-constrained composite minimization problems, with linear-exponential convergence proven for affine constraints via contraction theory.
A contraction-theory separation principle yields global exponential stability for controller-observer pairs and sharp LMI certificates for contractive RNNs, enabling stable output tracking and implicit neural network design.
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A Unified Control-Theoretic Framework for Saddle-Point Dynamics in Constrained Optimization
A PID feedback law on dual variables induces a unified family of saddle-point flows for constrained optimization, with explicit global exponential convergence guarantees under convexity and affine constraints.
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Proximal Gradient Dynamics and Feedback Control for Equality-Constrained Composite Optimization
PI-PGD dynamics have equilibria equivalent to stationary points of equality-constrained composite minimization problems, with linear-exponential convergence proven for affine constraints via contraction theory.
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A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning
A contraction-theory separation principle yields global exponential stability for controller-observer pairs and sharp LMI certificates for contractive RNNs, enabling stable output tracking and implicit neural network design.