Piecewise linear relationship between L1 norm objective functional values and L∞ norm constraint specifications - Miao, Qing; Ling, Bingo Wing-Kuen; Wang, Xiaoling (Digital signal processing, 2019)
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.