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• W2083042020 abstract "The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a root-finding algorithm for finding arbitrary points on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. Only matrix-vector operations are required. The primal-dual solution of this problem gives function and derivative information needed for the root-finding method. Numerical experiments on a comprehensive set of test problems demonstrate that the method scales well to large problems." @default.
• W2083042020 created "2016-06-24" @default.
• W2083042020 creator A5054518852 @default.
• W2083042020 creator A5091640094 @default.
• W2083042020 date "2009-01-01" @default.
• W2083042020 modified "2023-10-16" @default.
• W2083042020 title "Probing the Pareto Frontier for Basis Pursuit Solutions" @default.
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• W2083042020 doi "https://doi.org/10.1137/080714488" @default.
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