%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-01-08 17:00:14
 % @LastEditTime: 2021-01-10 09:07:05
%--------------------------
function x = quadratic_programming(A, b, Q_obj)
    % 1. compute initial feasible solution
    warning('off','all')
    x0 = A \ b; 
    warning('on','all')

    % 2. compute null-space matrix Z
    [~, SpRight] = spspaces(A, 3, 10^-10);
    Q = SpRight{1};
    J = SpRight{3};
    Z = Q(:,J); % null-space matrix of A        

    % Z = null(full(A)); % slow version

    % 3. compute step \omega
    L = Z' * Q_obj * Z;
    rhs = - Z' * Q_obj * x0;
    omega = L \ rhs;

    x = x0 + Z * omega;
end