Journal
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
Volume 51, Issue 2, Pages 1097-1106Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMC.2019.2894862
Keywords
Adaptive algorithm; directed graphs; projection algorithm; resource allocation
Funding
- National Natural Science Foundation of China [61673107]
- National Ten Thousand Talent Program for Young Top-Notch Talents [W2070082]
- General Joint Fund of the Equipment Advance Research Program of the Ministry of Education [6141A020223]
- National Science Foundation [ECCS-1611423]
- Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [BM2017002]
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This paper investigates resource allocation problem for a group of agents communicating over a strongly connected directed graph. Two continuous-time algorithms are proposed for weight-balanced and weight-unbalanced graphs, with convergence analysis and performance evaluation through numerical simulations.
This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms.
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