Distributed Saddle-Point Subgradient Algorithms With Laplacian Averaging

We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a sum of convex functions in the local variables of the agents...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 62; H. 6; S. 2720 - 2735
Hauptverfasser: Mateos-Nunez, David, Cortes, Jorge
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.06.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithm design and analysis
Algorithms
Computer simulation
Constraints
Convergence
Convex functions
Coupling
Decisions
Distributed optimization
Estimates
Graph theory
Iterative methods
Laplace equations
Laplacian averaging
Mathematical models
Minimization
multi-agent networks
Multipliers
Nonlinearity
Optimization
Run time (computers)
Saddle points
saddle-point algorithms
ISSN:0018-9286, 1558-2523
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Zusammenfassung:We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a sum of convex functions in the local variables of the agents. In the latter case, the proposed algorithm reduces to primal-dual updates using local subgradients and Laplacian averaging on local copies of the multipliers associated to the global constraints. For the case of general convex-concave saddle-point problems, our analysis establishes the convergence of the running time-averages of the local estimates to a saddle point under periodic connectivity of the communication digraphs. Specifically, choosing the gradient step-sizes in a suitable way, we show that the evaluation error is proportional to 1/√t, where t is the iteration step. We illustrate our results in simulation for an optimization scenario with nonlinear constraints coupling the decisions of agents that cannot communicate directly.
Bibliographie:ObjectType-Article-1
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2616646