forbes_svm.m

% FORBES_SVM
%
%   FORBES_SVM(A, b, lam, opt) solves the problem
%
%     minimize (lam/2)||x||^2 + sum(max(0, b.*(1-A*x))
%

function out = forbes_svm(A, b, lam0, opt)

%   % if options are not given
%   if nargin < 4, opt = struct(); end
% 
%   % set some defualt options
%   if ~isfield(opt, 'term'), opt.term = []; end
%   term0 = opt.term;
%   if ~isfield(opt, 'tol'), opt.tol = []; end
%   tol0 = opt.tol;
%   if ~isfield(opt, 'display'), opt.display = 0; end
% 
%   % compute Lipschitz constant
%   [m, n] = size(A);
%   eigsOpt.issym = 1;
%   eigsOpt.tol = 1e-3;
%   funHessian = @(x) A'*(A*x);
%   Lf = eigs(funHessian, n, 1, 'LM', eigsOpt);
%   opt.Lf = Lf;
% 
%   % to warm start or not to warm start?
%   if ~isfield(opt, 'continuation') || isempty(opt.continuation), opt.continuation = 1; end
%   if opt.continuation
%     lam_max = norm(A'*b,'inf');
%     lam = lam_max;
%   else
%     lam = lam0;
%   end
% 
%   %
%   f = quadLoss(1, zeros(m, 1));
%   init = zeros(n, 1);
% 
%   for i_cont = 1:100
% 
%     % % this is the continuation scheme of SpaRSA
%     % btilde = b-A*init;
%     % lam = max(0.5*norm(A'*btilde,'inf'), lam0);
% 
%     % this is the simpler continuation scheme
%     lam = max(0.5*lam, lam0);
% 
%     g = l1Norm(lam);
%     if lam <= lam0
%       opt.term = term0;
%       opt.tol = tol0;
%     else
%       opt.term = [];
%       opt.tol = 1e-3*lam;
%     end
%     out = forbes(f, g, init, {A, -b}, [], opt);
%     if lam <= lam0
%       break;
%     end
%     init = out.x;
%   end

end