L1-minimization has been one of the hot topics in the signal processing and optimization communities in the last five years. In the emerging compressive sensing (CS) theory, it has been shown to be an efficient approach to recover sparsest solutions to certain underdetermined systems of linear equations. Here I just share some useful online resources about L1-minimization problems as well as some state-of-the-art algorithms.
Berkeley University L1-benchmark
https://people.eecs.berkeley.edu/~yang/software/l1benchmark/
Stanford University SparseLab: http://sparselab.stanford.edu/
M. Li's Blog 