TY - CHAP

T1 - Decentralized consensus optimization and resource allocation

AU - Nedich, Angelia

AU - Olshevsky, Alexander

AU - Shi, Wei

N1 - Funding Information:
The work of A.N. and A.O. was supported by the Office of Naval Research grant N000014-16-1-2245. The work of A.O. was also supported by the NSF award CMMI-1463262 and AFOSR award FA-95501510394.
Funding Information:
Fig. 10.4 Plots of the normalized residual ‖x0−x∗‖F‖xk−x∗‖F. The step sizes for Mirror-Push-DIGing are roughly hand tuned. rc is the connectivity ratio and ra is the activation ratio Acknowledgements The work of A.N. and A.O. was supported by the Office of Naval Research grant N000014-16-1-2245. The work of A.O. was also supported by the NSF award CMMI-1463262 and AFOSR award FA-95501510394.
Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

PY - 2018

Y1 - 2018

N2 - We consider the problems of consensus optimization and resource allocation, and we discuss decentralized algorithms for solving such problems. By “decentralized”, we mean the algorithms are to be implemented in a set of networked agents, whereby each agent is able to communicate with its neighboring agents. For both problems, every agent in the network wants to collaboratively minimize a function that involves global information, while having access to only partial information. Specifically, we will first introduce the two problems in the context of distributed optimization, review the related literature, and discuss an interesting “mirror relation” between the problems. Afterwards, we will discuss some of the state-of-the-art algorithms for solving the decentralized consensus optimization problem and, based on the “mirror relationship”, we then develop some algorithms for solving the decentralized resource allocation problem. We also provide some numerical experiments to demonstrate the efficacy of the algorithms and validate the methodology of using the “mirror relation”.

AB - We consider the problems of consensus optimization and resource allocation, and we discuss decentralized algorithms for solving such problems. By “decentralized”, we mean the algorithms are to be implemented in a set of networked agents, whereby each agent is able to communicate with its neighboring agents. For both problems, every agent in the network wants to collaboratively minimize a function that involves global information, while having access to only partial information. Specifically, we will first introduce the two problems in the context of distributed optimization, review the related literature, and discuss an interesting “mirror relation” between the problems. Afterwards, we will discuss some of the state-of-the-art algorithms for solving the decentralized consensus optimization problem and, based on the “mirror relationship”, we then develop some algorithms for solving the decentralized resource allocation problem. We also provide some numerical experiments to demonstrate the efficacy of the algorithms and validate the methodology of using the “mirror relation”.

KW - Consensus optimization

KW - Convex constrained problems

KW - Decentralized algorithms

KW - Resource allocation

UR - http://www.scopus.com/inward/record.url?scp=85056630361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056630361&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-97478-1_10

DO - 10.1007/978-3-319-97478-1_10

M3 - Chapter

AN - SCOPUS:85056630361

T3 - Lecture Notes in Mathematics

SP - 247

EP - 287

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -