### Jorge Cortés

#### Professor

Distributed coordination for separable convex optimization with coupling constraints

S. K. Niederländer, J. Cortés

Proceedings of the IEEE Conference on
Decision and Control, Osaka, Japan, 2015, pp. 694-699

### Abstract

This paper considers a network of agents described by a weighted
undirected graph that seek to solve a convex optimization problem
with separable objective function and coupling equality and
inequality constraints. Both the objective function and the
inequality constraints are locally Lipschitz. We assume that the
constraints are compatible with the network topology in the sense
that, if the state of an agent is involved in the evaluation of any
given constraint, this agent is able to fully evaluate it with the
information provided by its neighbors. Building on the saddle-point
dynamics of an augmented Lagrangian function, we develop provably
correct distributed continuous-time coordination algorithms that
allow each agent to find their component of the optimal solution
vector along with the optimal Lagrange multipliers for the equality
constraints in which the agent is involved. Our technical approach
combines notions and tools from nonsmooth analysis, set-valued
dynamical systems, and convex programming.

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Mechanical and Aerospace Engineering,
University of California, San Diego

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Ph: 1-858-822-7930

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