MATLAB: Two linear equation with absolute value equation

equationnonlinear

Hello,
I have two linear equation and one absolute value equation. Is there a easy way to obtain minimum norm solution ?

Best Answer

Correct minimum norm solution is
xmin =
   90.0000
  -40.0000
    5.0000
    5.0000
normxmin =
   98.7421
obtained with this code
s = cell(1,4);
[s{:}] = ndgrid([-1 1]);
s = reshape(cat(5,s{:}),[],4);
fmin = Inf;
xmin = nan(4,1);
for k=1:size(s,1)
    sk = s(k,:);
    Aeq = [1 1 -1 -1;
           1 1 1 1;
           sk.*[1 1 -1 -1]];
    beq = [40; 60; 120];
    A = -diag(sk);
    b = zeros(4,1);
    [x,f,flag] = quadprog(eye(4), zeros(4,1), ...
        A, b, ...
        Aeq, beq, ...
        [], []);
    if flag > 0 && f < fmin
        fmin = f;
        xmin = x;
    end
end
xmin
normxmin = norm(xmin,2)
% Check the constraints
xmin(1)+xmin(2)-xmin(3)-xmin(4)
xmin(1)+xmin(2)+xmin(3)+xmin(4)
abs(xmin(1))+abs(xmin(2))-abs(xmin(3))-abs(xmin(4))
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