Abstract
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.
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