Error using barrier Objective function is undefined at initial point. Fmincon cannot continue.

Can anyone see why I get this error:

Error using barrier

Objective function is undefined at initial point. Fmincon cannot continue.

Error in fmincon (line 895)

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in untitled4 (line 19)

[x_opt, f_opt, exitflag] = fmincon(augmented_objective, x0, [], [], [], [], [], [], [], options);

When running this code:

main_function = @(x) (2*x(1) + x(2))^2 + x(2)^4 - 4*x(1) - 4*x(2);
constraints = @(x) [x(1)^2 + x(2)^2 - 4; -(4*x(1) + 5*x(2) - 4)];
max_it = 5;
x0 = [10; 10];  % Initial guess
Beta = 0.1;      % Initial penalty parameter
% Increase max iterations due to initial guess
options = optimoptions('fmincon', 'Display', 'iter', 'MaxIterations', 1000);
for it = 1:max_it
    % Define the barrier function
    barrier_function = @(x) -sum(log(constraints(x) + 1e-6));
    % Define the augmented objective function with the barrier term
    augmented_objective = @(x) main_function(x) + (1/Beta) * barrier_function(x);
    augmented_objective(x0)
    % Using fmincon to minimize the problem
    [x_opt, f_opt, exitflag] = fmincon(augmented_objective, x0, [], [], [], [], [], [], [], options);
    % Check if the optimization converged successfully
    if exitflag <= 0
        fprintf('Optimization did not converge at iteration %d.\n', it);
        break;
    end
    % Update the initial guess for the next iteration
    x0 = x_opt;
    Beta = Beta * 10;
    fprintf('Iteration %d: x_opt = [%.4f, %.4f], f_opt = %.4f\n', it, x_opt, f_opt);
end

ans = 1.0723e+04 - 3.1416e+01i

Error using barrier
Objective function is undefined at initial point. Fmincon cannot continue.

Error in fmincon (line 891)
[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Answer 1

[Torsten]

If you insert the line

augmented_objective(x0)

before the call to fmincon, you will see that your objective returns a complex number. This is forbidden in optimization problems.

The reason is that your constraint function takes "log" of a negative number.

[Tilde Netz]

Thank you so much! I still got error when I chaged that, but I rearranged the barrier function to be inside the augumented objective function and then it worked for some reason.