Distributed Subgradient Projection Algorithm Over Directed Graphs

We propose Directed-Distributed Projected Subgradient (D-DPS) to solve a constrained optimization problem over a multi-agent network, where the goal of agents is to collectively minimize the sum of locally known convex functions. Each agent in the network owns only its local objective function, cons...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 62; no. 8; pp. 3986 - 3992
Main Authors Chenguang Xi, Khan, Usman A.
Format Journal Article
LanguageEnglish
Published IEEE 01.08.2017
Subjects
Constrained optimization
Convergence
Convex functions
directed graphs
distributed optimization
Indexes
Linear matrix inequalities
Linear programming
Optimization
projected subgradient
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Summary:We propose Directed-Distributed Projected Subgradient (D-DPS) to solve a constrained optimization problem over a multi-agent network, where the goal of agents is to collectively minimize the sum of locally known convex functions. Each agent in the network owns only its local objective function, constrained to a commonly known convex set. We focus on the circumstance when communications between agents are described by a directed network. The D-DPS combines surplus consensus to overcome the asymmetry caused by the directed communication network. The analysis shows the convergence rate to be O( ln k /√k ).
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2615066