Piecewise linear relationship between L1 norm objective functional values and L∞ norm constraint specifications

For a sparse optimization problem with an L1 norm objective function subject to an L∞ norm inequality constraint, this paper finds that there is a piecewise linear relationship between the L1 norm objective functional values and the L∞ norm constraint specifications. This piecewise linear relationsh...

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Bibliographic Details
Published inDigital signal processing Vol. 92; pp. 234 - 240
Main Authors Miao, Qing, Ling, Bingo Wing-Kuen, Wang, Xiaoling
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2019
Subjects
[formula omitted]-minimization
[formula omitted]-norm constraint
Piecewise linear function
Sparse optimization
Sparse optimization
Piecewise linear function
L∞-norm constraint
L1-minimization
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ISSN1051-2004
1095-4333
DOI10.1016/j.dsp.2019.06.012

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Summary:For a sparse optimization problem with an L1 norm objective function subject to an L∞ norm inequality constraint, this paper finds that there is a piecewise linear relationship between the L1 norm objective functional values and the L∞ norm constraint specifications. This piecewise linear relationship is proved mathematically. Also, computer numerical simulations on a set of signal vectors verify the validity of this result. This result can provide a guidance for system analysts to define the specification on the L∞ norm specification.
ISSN:1051-2004
1095-4333
DOI:10.1016/j.dsp.2019.06.012