Proximal-Gradient Homotopy Method for Sparse Least Squares

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English
Proximal-gradient homotopy is an efficient numerical method for solving the L1-regularized least-squares problem—minimize_x (1/2) ||A*x-b||_2^2 + lambda*||x||_1—where A is an m-by-n matrix, and lambda is a positive regularization parameter. Last published: March 23, 2012.
  • Version:

    1.0

    File Name:

    PGH4SLS.zip

    Date Published:

    5/12/2016

    File Size:

    20 KB

      Proximal-gradient homotopy is an efficient numerical method for solving the L1-regularized least-squares problem—minimize_x (1/2) ||A*x-b||_2^2 + lambda*||x||_1—where A is an m-by-n matrix, and lambda is a positive regularization parameter. This method is especially effective for sparse recovery applications in which the dimensions satisfies m < n and the optimal solution x* is provably sparse. The implementation in MATLAB can solve the more general problem—minimize_x f(x) + lambda*R(x)—where f(x) is a differentiable convex function and R(x) is a simple convex function whose proximal mapping can be computed efficiently.
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