38 research outputs found
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
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
Linear Convergence of Primal-Dual Gradient Methods and their Performance in Distributed Optimization
In this work, we revisit a classical incremental implementation of the
primal-descent dual-ascent gradient method used for the solution of equality
constrained optimization problems. We provide a short proof that establishes
the linear (exponential) convergence of the algorithm for smooth
strongly-convex cost functions and study its relation to the non-incremental
implementation. We also study the effect of the augmented Lagrangian penalty
term on the performance of distributed optimization algorithms for the
minimization of aggregate cost functions over multi-agent networks