Distributed Continuous-Time Algorithm for Constrained Convex Optimizations via Nonsmooth Analysis Approach

This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost function and local constraint set, for the const...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 62; no. 10; pp. 5227 - 5233
Main Authors: Zeng, Xianlin, Yi, Peng, Hong, Yiguang
Format: Journal Article
Language:English
Published: IEEE 01.10.2017
Subjects:
Algorithm design and analysis
Constrained distributed optimization
continuous-time algorithms
Convergence
Cost function
Heuristic algorithms
Laplace equations
multi-agent systems
nonsmooth analysis
projected dynamical systems
Stability analysis
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost function and local constraint set, for the constrained optimization problem. Then we prove that all the agents of the algorithm can find the same optimal solution, and meanwhile, keep the states bounded while seeking the optimal solutions. We conduct a complete convergence analysis by employing nonsmooth Lyapunov functions for the stability analysis of differential inclusions. Finally, we provide a numerical example for illustration.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2628807