A tutorial on decomposition methods for network utility maximization
Abstract
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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- Authors
- Palomar, D. P., & Chiang, M.
- Affiliations
- Princeton University (US)
- Venue
- IEEE Journal on Selected Areas in Communications
- Published
- 2006-08
- Volume
- 24
- Issue
- 8
- Pages
- 1439-1451
- ISSN
- 0733-8716 (ISSN-L)
- OpenAlex
- W2162986857
- Cited by
- 1,647
- References
- 29
- Citations by year
- 2026: 24 · 2025: 30 · 2024: 33 · 2023: 41 · 2022: 63 · 2021: 68 · 2020: 100 · 2019: 109 · 2018: 117 · 2017: 133 · 2016: 151 · 2015: 102 · 2014: 127 · 2013: 128 · 2012: 106
- FWCI
- 43.53
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Journal on Selected Areas in Communications (publishedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Wireless Network Optimization
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Computer Science › Computer Networks and Communications › Network Traffic and Congestion Control
- Keywords
- network utility maximization, decomposition method, distributed resource allocation, Lagrange duality, convex optimization, subgradient method, primal decomposition, dual decomposition, hierarchical decomposition, partial decomposition, modular network design
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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