On Distributed Convex Optimization Under Inequality and Equality Constraints

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...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 57; no. 1; pp. 151 - 164
Main Authors: Minghui Zhu, Martinez, S.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptative systems
Algorithm design and analysis
Algorithms
Applied sciences
Asymptotic properties
Automatic control
Computer science; control theory; systems
Control theory. Systems
Convergence
Convex functions
Cooperative control
distributed optimization
Exact sciences and technology
Heuristic algorithms
Inequalities
Lagrangian functions
multi-agent systems
Network topology
Networks
Optimal control
Optimization
Saddle points
Studies
multi-agent systems
Subgradient optimization
distributed optimization
Cooperative control
Transmission protocol
Duality
Topology
Adaptive control
Convex programming
Saddle point
Penalty function
Multiagent system
Cooperation
Distributed algorithm
Inequality constraint
Equality constraint
Primal dual method
Distributed control
Asymptotic approximation
Objective function
Lagrangian function
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Description
Summary: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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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2167817