Mathematics > Optimization and Control
[Submitted on 3 Aug 2015 (v1), last revised 23 Mar 2016 (this version, v6)]
Title:Low-rank spectral optimization via gauge duality
View PDFAbstract:Various applications in signal processing and machine learning give rise to highly structured spectral optimization problems characterized by low-rank solutions. Two important examples that motivate this work are optimization problems from phase retrieval and from blind deconvolution, which are designed to yield rank-1 solutions. An algorithm is described that is based on solving a certain constrained eigenvalue optimization problem that corresponds to the gauge dual which, unlike the more typical Lagrange dual, has an especially simple constraint. The dominant cost at each iteration is the computation of rightmost eigenpairs of a Hermitian operator. A range of numerical examples illustrate the scalability of the approach.
Submission history
From: Michael Friedlander [view email][v1] Mon, 3 Aug 2015 05:05:12 UTC (1,166 KB)
[v2] Tue, 4 Aug 2015 21:32:41 UTC (1,166 KB)
[v3] Wed, 12 Aug 2015 23:21:38 UTC (1,168 KB)
[v4] Mon, 29 Feb 2016 23:49:13 UTC (1,173 KB)
[v5] Wed, 2 Mar 2016 18:41:29 UTC (1,173 KB)
[v6] Wed, 23 Mar 2016 17:05:13 UTC (1,170 KB)
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