An O(1/k) gradient method for network resource allocation problems

Amir Beck, Angelia Nedich, Asuman Ozdaglar, Marc Teboulle

Research output: Contribution to journalArticle

73 Citations (Scopus)

Abstract

We present a fast distributed gradient method for a convex optimization problem with linear inequalities, with a particular focus on the network utility maximization (NUM) problem. Most existing works in the literature use (sub)gradient methods for solving the dual of this problem which can be implemented in a distributed manner. However, these (sub)gradient methods suffer from an O(1/√k) rate of convergence (where k is the number of iterations). In this paper, we assume that the utility functions are strongly concave, an assumption satisfied by most standard utility functions considered in the literature. We develop a completely distributed fast gradient method for solving the dual of the NUM problem. We show that the generated primal sequences converge to the unique optimal solution of the NUM problem at rate O(1/k).

Original languageEnglish (US)
Article number6756941
Pages (from-to)64-73
Number of pages10
JournalIEEE Transactions on Control of Network Systems
Volume1
Issue number1
DOIs
StatePublished - Mar 1 2014
Externally publishedYes

Fingerprint

Gradient methods
Gradient Method
Resource Allocation
Utility Maximization
Resource allocation
Subgradient Method
Utility Function
Convex optimization
Convex Optimization
Linear Inequalities
Rate of Convergence
Optimal Solution
Optimization Problem
Converge
Iteration

Keywords

  • convex functions
  • Gradient methods
  • network utility maximization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization

Cite this

An O(1/k) gradient method for network resource allocation problems. / Beck, Amir; Nedich, Angelia; Ozdaglar, Asuman; Teboulle, Marc.

In: IEEE Transactions on Control of Network Systems, Vol. 1, No. 1, 6756941, 01.03.2014, p. 64-73.

Research output: Contribution to journalArticle

Beck, Amir ; Nedich, Angelia ; Ozdaglar, Asuman ; Teboulle, Marc. / An O(1/k) gradient method for network resource allocation problems. In: IEEE Transactions on Control of Network Systems. 2014 ; Vol. 1, No. 1. pp. 64-73.
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