On distributed convex optimization under inequality and equality constraints via primal-dual subgradient methods

Minghui Zhu and Sonia Martínez
IEEE Transactions on Automatic Control, 57 (1) (2012) 151-164

Abstract:

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms which are based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater's condition.

File: main.pdf

Bib-tex entry:

@article{MZ-SM:09c,
author = {M. Zhu and S. Mart{\'\i}nez},
title = {On distributed convex optimization under inequality and equality constraints via primal-dual subgradient methods},
journal= {IEEE Transactions on Automatic Control},
volume = 57,
number = 1,
pages = 151--164,
year = {2011}
}