### Jorge Cortés

#### Professor

Periodic and event-triggered communication for distributed
continuous-time convex optimization

S. S. Kia, J. Cortés, S. Martínez

Proceedings of the American Control Conference, Portland,
Oregon, USA, 2014, pp. 5010-5015

### Abstract

We propose a distributed continuous-time algorithm
to solve a network optimization problem where the
global cost function is a strictly convex function
composed of the sum of the local cost functions of
the agents. We establish that our algorithm, when
implemented over strongly connected and
weight-balanced directed graph topologies, converges
exponentially fast when the local cost functions are
strongly convex and their gradients are globally
Lipschitz. We also characterize the privacy
preservation properties of our algorithm and extend
the convergence guarantees to the case of
time-varying, strongly connected, weight-balanced
digraphs. When the network topology is a connected
undirected graph, we show that exponential
convergence is still preserved if the gradients of
the strongly convex local cost functions are locally
Lipschitz, while it is asymptotic if the local cost
functions are convex. We also study discrete-time
communication implementations. Specifically, we
provide an upper bound on the stepsize of a
synchronous periodic communication scheme that
guarantees convergence over connected undirected
graph topologies and, building on this result,
design a centralized event-triggered implementation
that is free of Zeno behavior. Simulations
illustrate our results.

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Mechanical and Aerospace Engineering,
University of California, San Diego

9500 Gilman Dr,
La Jolla, California, 92093-0411

Ph: 1-858-822-7930

Fax: 1-858-822-3107

cortes at ucsd.edu

Skype id:
jorgilliyo