Abstract
A new first-order optimality condition for the basis pursuit denoise (BPDN) problem is derived. This condition provides a new approach to choose the penalty parameters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.
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Project supported by the National Natural Science Foundation of China (No. 61271014), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20124301110003), and the Graduated Students Innovation Fund of Hunan Province (No.CX2012B238)
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Zhu, W., Shu, S. & Cheng, Lz. First-order optimality condition of basis pursuit denoise problem. Appl. Math. Mech.-Engl. Ed. 35, 1345–1352 (2014). https://doi.org/10.1007/s10483-014-1860-9
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DOI: https://doi.org/10.1007/s10483-014-1860-9