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Near-ideal behavior of a modified Elastic Net algorithm

In this paper it is shown that a modification of the Elastic Net algorithm (MEN) exhibits near ideal behavior in the following sense: Suppose the input to the algorithm is a vector of known sparsity index but unknown locations for the nonzero components. Then the output error of the algorithm is bounded by a universal constant times the error achieved by an oracle that knows not just the sparsity index but also the locations of the nonzero components. This result generalizes an earlier result of Candès and Plan on the near ideal behavior of the LASSO algorithm.