Matlab: fmincon converging to infeasible point, not meeting equality constraint - matlab

Question

I am trying to use fmincon to optimize x such that R*x is minimized while x can be values between 0 and 1.5 and the sum(x) = 3
R = transpose([6 6 6 6 6 6 6 9 9 9 9 13 13 13 13 9 9 9 9 6 6 6 6 6]);
x0 = zeros(24,1);
f='0';
for j=1:24
s='%d*x(%d)';
s=sprintf(s,R(j),j);
g='%s+%s';
f=sprintf(g,f,s);
end
A = ones(2,24);
A(2,:) = -1;
b = [1.5; 0]; % Want x's to be between 0 and 1.5
Aeq = ones(1,24);
beq = [3];
%Bounds
lb = zeros(24,1);
ub = ones(24,1);
x = fmincon(f, x0, A, b,Aeq, beq,lb,ub);
I want the sum of x to equal 3 (attempted to show this with equivalency matrices Aeq and beq). The following error was shown when I run the code:
converged to an infeasible point
It should be noted that this code shows that sum(x) = 2.25 instead of sum(x) = 3

Answer 1

First, your function definition can be shortened to:
R = [6 6 6 6 6 6 6 9 9 9 9 13 13 13 13 9 9 9 9 6 6 6 6 6];
f = #(x)R*x;
Second, your initial point x0 does not satisfy your constraints, so let's change it to:
x0 = zeros(24,1)+3/24;
so that the sum of x is equal to 3.
Next, since you have a constant upper and lower bounds on x, you don't need to use A and b matrices, so we get rid of them and replace them with empty matrices []. We will rely only on lb and ub instead:
lb = zeros(24,1);
ub = 1.5*ones(24,1);
Finally, we start fmincon by using
x = fmincon(f, x0,[],[],Aeq, beq,lb,ub)
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the optimality tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
x =
0.2500
0.2500
0.2500
0.2500
0.2500
0.2500
0.2500
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.2500
0.2500
0.2500
0.2500
0.2500