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I am playing with some Compressed Sensing (think single pixel camera) applications and would like to have a Mathematica equivalent of a Matlab package call Convex Optimization (CVX). Specifically, I am solving an underdetermined, constrained, L1Norm minimization problem. I have been using NMinimize, but it very slow compared to the Matlab code written by a colleague. I don’t want to give him the pleasure of thinking Matlab is superior. I am sure that the long run times are due to my poor programing skills. The solution is sparse but I do not know how to add that as an additional constraint. Anyway, seems I can’t find a good reference for compressed sensing in Mathematica. Any suggestions would be great!

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For a convex optimization problem FindMinimum is likely to be much faster than NMinimize. –  Daniel Lichtblau Jul 31 '14 at 23:33

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