Equivalence and Strong Equivalence Between the Sparsest and Least $$\ell _1$$ ℓ 1 -Norm Nonnegative Solutions of Linear Systems and Their Applications
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چکیده
منابع مشابه
Equivalence and Strong Equivalence between Sparsest and Least `1-Norm Nonnegative Solutions of Linear Systems and Their Application
Many practical problems can be formulated as `0-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative solutions to underdetermined linear systems. Recent study indicates that `1-minimization is efficient for solving some classes of `0-minimization problems. From a mathematical point of view, however, the understanding of the relationship between `0and `1-mini...
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RSP-Based Analysis for Sparsest and Least $\ell_1$-Norm Solutions to Underdetermined Linear Systems
Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does l1-minimization find the sparsest solution to an underdetermined linear system? In this paper, a deterministic analysis, rooted in the classic linear programming theory, is carried out to further address this question. We first identify a necess...
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Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does l1-minimization find the sparsest solution to an underdetermined linear system? In this paper, a deterministic analysis, rooted in the classic linear programming theory, is carried out to further address this question. We first identify a necess...
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ژورنال
عنوان ژورنال: Journal of the Operations Research Society of China
سال: 2014
ISSN: 2194-668X,2194-6698
DOI: 10.1007/s40305-014-0043-1