Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 57, Issue 1, Pages 151-164Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2011.2167817
Keywords
Cooperative control; distributed optimization; multi-agent systems
Funding
- NSF CAREER [CMS-0643673, NSF IIS-0712746]
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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.
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