Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (10): 1345-1352.doi: https://doi.org/10.1007/s10483-014-1860-9

• Articles • Previous Articles    

First-order optimality condition of basis pursuit denoise problem

Wei ZHU1, Shi SHU1,2, Li-zhi CHENG3   

  1. 1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, P. R. China;
    2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan Province, P. R. China;
    3. Department of Mathematics and Computational Science, College of Science, National University of Defense Technology, Changsha 410073, P. R. China
  • Received:2013-06-28 Revised:2014-02-28 Online:2014-10-01 Published:2014-10-01
  • Supported by:
    Project supported by the National Natural Science Foundation of China (No. 61271014), the Special- ized Research Fund for the Doctoral Program of Higher Education (No. 20124301110003), and the Graduated Students Innovation Fund of Hunan Province (No.CX2012B238)

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 param- eters 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.

Key words: matrix completion, basis pursuit denoise (BPDN), fixed point iteration, first-order optimality

2010 MSC Number: 

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