Cutting Planes for Low-Rank-Like Concave Minimization Problems

2004 ◽  
Vol 52 (6) ◽  
pp. 942-953 ◽  
Author(s):  
Marcus Porembski
Keyword(s):  
Cutting Planes ◽  
Concave Minimization ◽  
Low Rank ◽  
Minimization Problems

Weighted lp − l1 minimization methods for block sparse recovery and rank minimization

2020 ◽  
pp. 1-19
Author(s):  
Yun Cai
Keyword(s):  
Sparse Recovery ◽  
Low Rank ◽  
Sparse Signals ◽  
Rank Minimization ◽  
Linear Measurements ◽  
L1 Minimization ◽  
Minimization Problems ◽  
Theoretical Support ◽  
Minimization Methods ◽  
Noisy Measurements

This paper considers block sparse recovery and rank minimization problems from incomplete linear measurements. We study the weighted [Formula: see text] [Formula: see text] norms as a nonconvex metric for recovering block sparse signals and low-rank matrices. Based on the block [Formula: see text]-restricted isometry property (abbreviated as block [Formula: see text]-RIP) and matrix [Formula: see text]-RIP, we prove that the weighted [Formula: see text] minimization can guarantee the exact recovery for block sparse signals and low-rank matrices. We also give the stable recovery results for approximately block sparse signals and approximately low-rank matrices in noisy measurements cases. Our results give the theoretical support for block sparse recovery and rank minimization problems.

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