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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Use the following first guess values
x0 = [1; 1; 0; 1; 1]; % [x y z lambda1 lambda2]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Use the following options for the solver
options = optimoptions("fsolve", "MaxFunctionEvaluations", 10000, "MaxIterations", 10000);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fun=fsolve(@kkt_system,x0,options);
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% Test if the function is written
% correctly by saving its output inside
% the following variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
F_test = kkt_system(x0);
x_test =fun(1);
y_test =fun(2) ;
z_test =fun(3);
lambda1_test =(4);
lambda2_test =(5);
fprintf('x= %.1f \n', fun(1));
fprintf('y= %.1f \n', fun(2));
fprintf('z= %.1f \n', fun(3));
fprintf('lambda1= %.1f \n', fun(4));
fprintf('lambda2= %.1f \n', fun(5));

% Save the solution inside the following variables
x_opt = ;
y_opt = ;
z_opt = ;
lambda1_opt = ;
lambda2_opt = ;

function F = kkt_system(var)
x=var(1);
y=var(2);
z=var(3);
lambda1=var(4);
lambda2=var(5);
F=(var(1))^2+2*(var(2))^2+3*(var(3))^2-var(4)*(var(1)+var(2)+var(3)-2)-var(5)*(var(1)*var(2)+var(2)*var(3)-1);
end
function I=equazioni_Lagrange(w)
x=w(1);
y=w(2);
z=w(3);
lambda=w(4);
lambda=w(5);