I have a L1 minimization problem. I was trying to do it using CVX. In Matlab I have
function [ev,x] = L1minimizationV3( A, b, gamma )
% Computes x such that it minimizes the quantity norm(Ax-b,1).
% Uses slack variables
[m,n]=size(A);
lb=[zeros(n,1);zeros(n,1); zeros(2*m,1)];
I = eye(m);
Aeq = [A,-A,-I,I];
f=[ones(2n,1);gammaones(2m,1)];
options = optimoptions(‘linprog’,‘Algorithm’,‘dual-simplex’,‘OptimalityTolerance’,1e-10);
xps = linprog(f,[],[],Aeq,b,lb,[],options);
x=xps(1:2n);
ev=xps(1:n)-xps(n+1:2*n);
end
I was going to attempt this as
function L1minizationV4(A, b, gamma)
%
%
[m,n]=size(A);
lb=[zeros(n,1);zeros(n,1); zeros(2*m,1)];
I = eye(m);
Aeq = [A,-A,-I,I];
f=[ones(2n,1);gammaones(2*m,1)];
cvx_begin
variable x(n)
dual variable y;
minimize ( f’*x);
subject to y: A * x == b
cvx_end
I am not sure about the rest of the constraints.