Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/20697
Title: Gauge optimization and duality
Authors: Friedlander, MP
Macedo, I
Pong, TK
Keywords: Convex optimization
Duality
Gauges
Nonsmooth optimization
Issue Date: 2014
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM Journal on optimization, 2014, v. 24, no. 4, p. 1999-2022 How to cite?
Journal: SIAM journal on optimization 
Abstract: 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.
URI: http://hdl.handle.net/10397/20697
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/130940785
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