Gauge optimization and duality

Michael P. Friedlander, Ives Macedo, Ting Kei Pong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)


Unauthorized reproduction of this article is prohibited. Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by [R. M. Freund, Math. Programming, 38(1987), pp. 47-67], seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be used to model a remarkable array of useful problems, including a special case of conic optimization, and related problems that arise in machine learning and signal processing. The gauge structure of these problems allows for a special kind of duality framework. This paper explores the duality framework proposed by Freund, and proposes a particular form of the problem that exposes some useful properties of the gauge optimization framework (such as the variational properties of its value function), and yet maintains most of the generality of the abstract form of gauge optimization.
Original languageEnglish
Pages (from-to)1999-2022
Number of pages24
JournalSIAM Journal on Optimization
Issue number4
Publication statusPublished - 3 Dec 2014


  • Convex optimization
  • Duality
  • Gauges
  • Nonsmooth optimization

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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