Continuous-Time Distributed Subgradient Algorithm for Convex Optimization With General Constraints

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1694-1701
Journal / PublicationIEEE Transactions on Automatic Control
Volume64
Issue number4
Online published2 Jul 2018
Publication statusPublished - Apr 2019

Abstract

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch-Kuhn-Tucker (KKT) condition. By using tools from nonsmooth analysis and setvalued function theory, it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis.

Research Area(s)

  • Continuous-time subgradient algorithm, distributed convex optimization, multi-agent systems, nonsmooth analysis