384 research outputs found
Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization
Primal-dual gradient dynamics that find saddle points of a Lagrangian have
been widely employed for handling constrained optimization problems. Building
on existing methods, we extend the augmented primal-dual gradient dynamics
(Aug-PDGD) to incorporate general convex and nonlinear inequality constraints,
and we establish its semi-global exponential stability when the objective
function is strongly convex. We also provide an example of a strongly convex
quadratic program of which the Aug-PDGD fails to achieve global exponential
stability. Numerical simulation also suggests that the exponential convergence
rate could depend on the initial distance to the KKT point
Coordination of passive systems under quantized measurements
In this paper we investigate a passivity approach to collective coordination
and synchronization problems in the presence of quantized measurements and show
that coordination tasks can be achieved in a practical sense for a large class
of passive systems.Comment: 40 pages, 1 figure, submitted to journal, second round of revie
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