Problem using fminbnd function

The question gives the equation , and asks to generate a user-defined function for n=2 and 6; with n being the input vector and r being the output vector. The r value ranges from 1 to 5. It also asks to graph the U(r) curve for each n on the same plot and mark the points of the minimum.

I wrote this code:

function r_min=Problem_4_15(n,r1,r2)
close all
U=@(x)4*((1/x).^(2.*n) - (1/x).^(n));
options=optimset('Display','iter');
[r_min,U_min]=fminbnd(U,r1,r2,options); % Error Occurrence Line
rg=linspace(r1,r2);
Ug=U(rg);
plot(rg,Ug,r_min,U_min,'o')
grid on
xlabel('Distance Intermolecular r*')
ylabel('Potential Energy U')
title('Lennard-Jones-type dimensionless')
legend('function U','minimum r')

Matlab reports the following error:

Problem_4_15([2 6], 1, 5)
Error using fminbnd (line 238)
User supplied objective function must return a scalar value.

Error in Problem_4_15 (line 5)
[r_min,U_min]=fminbnd(U,r1,r2,options);

Part of the fminbnd function code, where line 238 appears:

% Check that the objective value is a scalar
if numel(fx) ~= 1
   error('MATLAB:fminbnd:NonScalarObj',... % Line 238
    getString(message('MATLAB:optimfun:fminbnd:NonScalarObj')));
end

How can I solve this problem to make the code work?

Thanks in advance.

Answer 1

[Alan Weiss]

All optimization solvers require that the objective function return a scalar value. You need to write your objective function in a way that it returns a scalar, not a vector or an array.

If you are trying to solve for a variety of parameter values, well, you will have to write a loop and solve for one parameter value at a time.

Alan Weiss

MATLAB mathematical toolbox documentation