Journal
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
Volume 50, Issue 7, Pages 2612-2622Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMC.2018.2823901
Keywords
Optimization; Convergence; Linear programming; Convex functions; Multi-agent systems; Generators; Couplings; Distributed convex optimization; geometric convergence; multiagent systems; primal-dual algorithm; time-varying directed graphs
Funding
- Special Financial Grant from China Post-Doctoral Science Foundation [2017T100670, 2016M590852]
- National Natural Science Foundation of China [61773321, 61673080]
- Innovation Support Program for Chongqing Overseas Returnees [cx2017043]
- Qatar National Research Fund (a member of Qatar Foundation) [NPRP 8-274-2-107]
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This paper studies a class of distributed convex optimization problems by a set of agents in which each agent only has access to its own local convex objective function and the estimate of each agent is restricted to both coupling linear constraint and individual box constraints. Our focus is to devise a distributed primal-dual gradient algorithm for working out the problem over a sequence of time-varying general directed graphs. The communications among agents are assumed to be uniformly strongly connected. A column-stochastic mixing matrix and a fixed step-size are applied in the algorithm which exactly steers all the agents to asymptotically converge to a global optimal solution. Based on the standard strong convexity and the smoothness assumptions of the objective functions, we show that the distributed algorithm is capable of driving the whole network to geometrically converge to an optimal solution of the convex optimization problem only if the step-size does not exceed some upper bound. We also give an explicit analysis for the convergence rate of the proposed optimization algorithm. Simulations on economic dispatch problems and demand response problems in power systems are performed to illustrate the effectiveness of the proposed optimization algorithm.
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