solver_LASSO.m

function [ x, out, opts ] = solver_LASSO( A, b, tau, x0, opts )
% SOLVER_LASSO Minimize residual subject to l1-norm constraints.
% [ x, out, opts ] = solver_LASSO( A, b, tau, x0, opts )
%    Solves the LASSO in the standard Tibshirani formulation,
%        minimize (1/2)*norm(A*x-b)^2
%        s.t.     norm(x,1) <= tau
%    A must be a linear operator or matrix, and b must be a vector. The
%    initial point x0 and the options structure opts are optional.
%
%   Note: many people use "LASSO" to refer to the problem:
%       minimize 1/2*norm(A*x-b)^2 + lambda*norm(x,1)
%   In TFOCS, this version is implemented in "solver_L1RLS"
%   (which stands for "L1 regularized Least Squares" )
%
%    If "nonneg" is a field in "opts" and opts.nonneg is true,
%       then the constraint x >= 0 is also imposed
%
% See also solver_L1RLS.m, solver_sBPDN.m

% Supply default values
error(nargchk(3,5,nargin));
if nargin < 4, x0 = []; end
if nargin < 5, opts = []; end
if ~isfield( opts, 'restart' ), opts.restart = 100; end

nonneg = false;
if isfield(opts,'nonneg')
    nonneg  = opts.nonneg;
    opts = rmfield(opts,'nonneg');
end
if isfield(opts,'nonNeg')
    nonneg  = opts.nonNeg;
    opts = rmfield(opts,'nonNeg');
end

if nonneg
    proj    = proj_simplex(tau);
else
    proj    = proj_l1(tau);
end

% Extract the linear operators
[x,out,opts] = tfocs( smooth_quad, { A, -b }, proj, x0, opts );

% TFOCS v1.3 by Stephen Becker, Emmanuel Candes, and Michael Grant.
% Copyright 2013 California Institute of Technology and CVX Research.
% See the file LICENSE for full license information.