A tutorial on decomposition methods for network utility maximization

A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison a...

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Bibliographic Details
Published in:IEEE journal on selected areas in communications Vol. 24; no. 8; pp. 1439 - 1451
Main Authors: Palomar, D.P., Mung Chiang
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2006
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Congestion control
cross-layer design
Decomposition
Decoupling
Design engineering
distributed algorithm
Distributed algorithms
Distributed computing
Distributed control
Jacobian matrices
Lagrangian functions
Mathematical analysis
Maximization
network architecture
network control by pricing
network utility maximization
Networks
optimization
Power control
Resource allocation
Resource management
Studies
Tutorial
Utilities
Utility programs
ISSN:0733-8716, 1558-0008
Online Access:Get full text
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Summary:A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable
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ISSN:0733-8716
1558-0008
DOI:10.1109/JSAC.2006.879350