MATLAB: Fmincon, the size of the current step is less than the value of the step size tolerance, but constraints are not satisfied

fminconoptimizationOptimization Toolbox

hi, I am working on a non-linear optimization problem.
I try to find the upper bound with fmincon, then currently facing this problem:
fmincon stopped because the size of the current step is less than the value of the step size tolerance but constraints are not satisfied to within the value of the constraint tolerance.
And I have to formulated it in the following way
Here is my current code:
H = zeros(4);
H(3,3) = 1; H(4,4) = 1;
c = [1 1 0 0]';
Q1 = zeros(4); Q1(1, 2) = 0.5; Q1(2, 1) = 0.5; Q1(2, 3) = 0.5; Q1(3, 2) = 0.5;
Q2 = zeros(4); Q2(1, 2) = 0.5; Q2(2, 1) = 0.5;
Q3 = zeros(4); Q3(2, 3) = 0.5; Q3(3, 2) = 0.5;
Q = [Q1; Q2; Q3];
A = zeros(3,4); A(2,4) = 1; A(3,1) = 1;
b = [2 3 5]';
lb = [0 0 0 0]'; ub = [10 4 10 10]';
objective = @(x) x'*H*x + c'*x;
x_0 = 0.5 * (lb + ub); % Use average as initial value
A_nlp = [];   b_nlp = [];
Aeq_nlp = []; beq_nlp = [];
function [c, c_eq] = NonLinearConstraint(x)
    c = []; % No nonlinear inequalities    
    for i = 1:m % Loop over the matrices defining the quadratic constraints
        Qi = Q((i-1)*n+1:i*n,:);
        c_eq(i)= x'*Qi*x - A(i,:)*x - b(i);
    end
end
nonlcon = @NonLinearConstraint;
options = optimoptions('fmincon','Display','iter','Algorithm','sqp');
[~, fval] = fmincon(objective, x_0, A_nlp, b_nlp, Aeq_nlp, beq_nlp, lb, ub, nonlcon, options);
It could not satisfy the constraint function. I also tried a few other optimoptions (different algorithm, step size ..)
Could anyone give me some advice how to fix this?
Thank you for your time!

Best Answer

I beleive the correct sign of A is "+" 
c_eq(i)= x'*Qi*x + A(i,:)*x - b(i);
Related Question