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On Distributed Convex Optimization Under Inequality and Equality Constraints

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2 Author(s)
Minghui Zhu ; Department of Mechanical and Aerospace Engineering, University of California, San Diego, United States of America ; Sonia Martinez

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 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 dynamically 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.

Published in:

IEEE Transactions on Automatic Control  (Volume:57 ,  Issue: 1 )