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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(More)
We establish several new existence theorems for nonlinear variational inequalities with generalized positively homogeneous functions. The results presented here are general enough to include two Mor e existence theorems of complementarity problems as the special cases. We also establish an existence result for the nonlinear complementarity problem with an(More)
It is well known that the so-called first-order predictor-corrector methods working in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. However, the best known iteration complexity of this type of methods is O (
A novel high-performance liquid chromatography (HPLC) method based on the internal standard method was established for assaying the tumour necrosis factor-α converting enzyme (TACE) activity and matrix metalloprotease-9 (MMP-9) activity, and was used to evaluate the inhibitive effectiveness of inhibitors to TACE and MMP-9. In the assay method for TACE and(More)
This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of several special cases such as nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems, and then two suucient existence conditions, are established for(More)
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(More)
This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems are established for this class of nonlinear projection equations. We utilize one of the(More)
Compressed sensing is a relatively new signal processing technique whereby the limits proposed by the Shannon-Nyquist theorem can be exceeded under certain conditions imposed upon the signal. Such conditions occur in many real-world scenarios, and compressed sensing has emerging applications in medical imaging, big data, and statistics. Finding practical(More)
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