### Jorge Cortés

#### Professor

Network optimization via smooth exact penalty functions enabled by
distributed gradient computation

P. Srivastava, J. Cortés

IEEE Transactions on Control of Network Systems, to appear

### Abstract

This paper proposes a distributed algorithm for a
network of agents to solve an optimization problem
with separable objective function and locally
coupled constraints. Our strategy is based on
reformulating the original constrained problem as
the unconstrained optimization of a smooth
(continuously differentiable) exact penalty
function. Computing the gradient of this penalty
function in a distributed way is challenging even
under the separability assumptions on the original
optimization problem. Our technical approach shows
that the distributed computation problem for the
gradient can be formulated as a system of linear
algebraic equations defined by separable problem
data. To solve it, we design an exponentially fast,
input-to-state stable distributed algorithm that
does not require the individual agent matrices to be
invertible. We employ this strategy to compute the
gradient of the penalty function at the current
network state. Our distributed algorithmic solver
for the original constrained optimization problem
interconnects this estimation with the prescription
of having the agents follow the resulting
direction. Numerical simulations illustrate the
convergence and robustness properties of the
proposed algorithm.

pdf

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