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2016

Asymptotic convergence of constrained primal-dual dynamics

1 years 21 days ago
Asymptotic convergence of constrained primal-dual dynamics
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.
Ashish Cherukuri, Enrique Mallada, Jorge Cort&eacu
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SCL
Authors Ashish Cherukuri, Enrique Mallada, Jorge Cortés
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