Fmincon - error using barrier

Hi,

I have a minimisation problem that I am trying to solve using matlab. I am pretty new to the general optimization toolbox and I dont fully understand all of the functions in it, such as the barrier function. I am getting the following error:

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

Error in fmincon (line 861)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in main (line 43)
    [x,fvals] = fmincon(obj,nvars,[],[],[],[],LB,UB,@constraint);

From what I understand the error is coming from the fact that my objective function is non-real at the starting postion, but I tried fixing it by making obj real using real(obj), and yet it doesnt work.

My code is as follows:

%% Parameters
l_0 = 3;
R = 5;
r=0.15*R:0.0425*R:R;
aoa = 15; %need to make a matrix out of this for the baseline blade
x = [4 5];

nvars = [2 3];
LB = [1 1];
UB = [5 6];

%% Constraint
function[c,ceq] = constraint(x,F,l_i)
l_i = 4;
F = 2;
c = (x(1)^2) * F + x(2) * l_i.^2 - x(2) * x(1) * l_i.^2 - x(1);
ceq = [];
end

%% Loop
k = 0;
for i = 1:length(r)
    
    l_i = (l_0 * r(i)) / R;
%     disp(l_i)
    phi = atan(((1 - x(1)) / (1 + x(2))) * (1/l_i(i)));
%     disp(phi)
    f = B / 2 * ((R - r(i)) / (R * sin(phi(i))));
%     disp(f)
    F = 2 / pi * acos(exp(1).^(-f(i)));
%     disp(F)
    
    twist_angle = phi(i) - aoa(i);
   
%     disp(twist_angle)
    obj = @(x)(8/((l_i).^2))*x(2)*(x(1)-1)*F*(l_i).^3;
%     disp(obj)
    
    [x,fvals] = fmincon(obj,nvars,[],[],[],[],LB,UB,@constraint);
    
    k = k+1;
end

Any help would be greatly appreciated.

[Matt J]

Reorganizing and running your code below leads to an error because B has not been provided.

%% Parameters
l_0 = 3;
R = 5;
r=0.15*R:0.0425*R:R;
aoa = 15; %need to make a matrix out of this for the baseline blade
x = [4 5];

nvars = [2 3];
LB = [1 1];
UB = [5 6];

%% Loop
k = 0;
for i = 1:length(r)
    
    l_i = (l_0 * r(i)) / R;
%     disp(l_i)
    phi = atan(((1 - x(1)) / (1 + x(2))) * (1/l_i(i)));
%     disp(phi)
    f = B / 2 * ((R - r(i)) / (R * sin(phi(i))));
%     disp(f)
    F = 2 / pi * acos(exp(1).^(-f(i)));
%     disp(F)
    
    twist_angle = phi(i) - aoa(i);
   
%     disp(twist_angle)
    obj = @(x)(8/((l_i).^2))*x(2)*(x(1)-1)*F*(l_i).^3;
%     disp(obj)
    
    [x,fvals] = fmincon(obj,nvars,[],[],[],[],LB,UB,@constraint);
    
    k = k+1;
end

Unrecognized function or variable 'B'.

%% Constraint
function[c,ceq] = constraint(x,F,l_i)
l_i = 4;
F = 2;
c = (x(1)^2) * F + x(2) * l_i.^2 - x(2) * x(1) * l_i.^2 - x(1);
ceq = [];
end