problem running fmincon, 'Input arguments to function include colon operator.'

I am trying to run fmincon and i get this error:

'Input arguments to function include colon operator.

To input the colon character, use ':' instead.'

I cannot understand why I get this error.

My code is below.

Anyone any ideas? Thank you.

 % code
  low_b = zeros(size(param));
options = optimoptions('fmincon', ...
    'Algorithm','interior-point', ...   
    'DerivativeCheck', 'on',...   
    'GradObj', 'on',...
    'HessFcn', @hessfh, ...
    'Hessian', 'user-supplied',...
    'Display','final');
[xfinal,fval,exitflag,output] = fmincon(@fh,[0.1;0.1],[],[],[],[],low_b,[],[],options);

 % code 
function [f,gradfh]=fh(param)
syms param1 param2 real
param=[param1;param2];
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2 
f = matlabFunction(f3,'vars',{param});
gradf3 = jacobian(f3,param).';
gradfh = matlabFunction(gradf3,'vars',{param});
end

    % code
function hessf=hessfh(param)
syms param1 param2 real
param=[param1;param2]
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2 
gradf3 = jacobian(f3,param).';
hessf3 = jacobian(gradf3,param);
hessf = matlabFunction(hessf3,'vars',{param});
end

Answer 1

[Walter Roberson]

The second output of the objective function should be the gradient evaluated at the input point, not a function handle. Likewise the hessian should be the value of the hessian, not a function handle.

[Ekin Ceyda Cetin]

If I do not use the gradient and hessian as function handle,

then i get the error from 'deal'.

'Error using deal

The number of outputs should match the number of inputs.'

Any suggestions in this situation?

    % code
syms param1 param2
param=[param1;param2];
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2;
gradf3 = jacobian(f3,param).';
fh = matlabFunction(f3,gradf3,'vars',{param});
hessf3 = jacobian(gradf3,param);
hessfh = matlabFunction(hessf3,'vars',{param});
low_b = zeros(size(param));
options = optimoptions('fmincon', ...
    'Algorithm','interior-point', ...   
    'DerivativeCheck', 'on',...   
    'GradObj', 'on',...
    'HessFcn', hessfh, ...
    'Hessian', 'user-supplied',...
    'Display','final');
[xfinal,fval,exitflag,output] = fmincon(fh,[0.1;0.1],[],[],[],[],low_b,[],[],options);

[Walter Roberson]

https://www.mathworks.com/help/optim/ug/fmincon.html#busxd7j-1

Your objective should only return the second output when it is requested. You will need to use a utility function to make the decision.

[Ekin Ceyda Cetin]

In the example, it uses function handle. That is so confusing. Is it possible to make the objective function return the second output when it is requested without a function handle?

Thank you for all the answers btw.

[Walter Roberson]

You have to pass a function handle to fmincon. However the function being called needs to check nargout and not return a second value when it is not asked for. When you use deal() it always wants as many left hand outputs as you have on the right hand.

You can write a small auxiliary function to do the work.

function [a, b] = oneOrTwo(t, y, f, g) 
 a = f(t, y);
 if nargout > 1
   b = g(t, y) ;
 end

Then

fmincon(@(t, y) oneOrTwo(t, y,  f, gradfh),......)

[Ekin Ceyda Cetin]

I tried to do as you say, I am getting colon operator error as I get in the beginning.

'Input arguments to function include colon operator. To input the colon character, use ':' instead.'

What am I doing wrong? Obviously I am missing sth but don't know what.

% code
syms param1 param2
param=[param1;param2];
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2;
gradf3 = jacobian(f3,param).';
hessf3 = jacobian(gradf3,param);
hessfh = matlabFunction(hessf3,'vars',{param});
low_b = zeros(size(param));
options = optimoptions('fmincon', ...
  'Algorithm','interior-point', ...   
  'DerivativeCheck', 'on',...   
  'GradObj', 'on',...
  'HessFcn', hessfh, ...
  'Hessian', 'user-supplied',...
  'Display','final');
[xfinal,fval,exitflag,output] = fmincon(@(param) fh(param, f, gradfh),[0.1;0.1],[],[],[],[],low_b,[],[],options);

    % code
function [f,gradfh]=fh(param, f, gradfh)
syms param1 param2
param=[param1;param2];
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2 
f = matlabFunction(f3,'vars',{param})
if nargout > 1 % gradient required
    gradf3 = jacobian(f3,param).';
    gradfh = matlabFunction(gradf3,'vars',{param});
end
end

[Walter Roberson]

Your fh is returning function handles. It needs to return numeric values.

[Ekin Ceyda Cetin]

Do you mean, i need to use the function handle just to make the choice of calculating only objective function or calculating gradient as well if necessary? I tried that too, not enough input arguments. Is this what you mean?

So sorry for being such a trouble :'

% code
syms param1 param2
param=[param1;param2];
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2;
f = matlabFunction(f3,'vars',{param});
gradf3 = jacobian(f3,param).';
gradfh = matlabFunction(gradf3,'vars',{param});
hessf3 = jacobian(gradf3,param);
hessfh = matlabFunction(hessf3,'vars',{param});
low_b = zeros(size(param));
param0=[3.6;2.6];
options = optimoptions('fmincon', ...
  'Algorithm','interior-point', ...   
  'DerivativeCheck', 'on',...   
  'GradObj', 'on',...
  'HessFcn', hessfh, ...
[xfinal,fval,exitflag,output] = fmincon(@(param1, param2) oneOrTwo(param1, param2,f,gradfh),param0,[],[],[],[],low_b,[],[],options);

% code
function [a, b] = oneOrTwo(c, d, h, g) 
syms c d
a = h(c,d);
if nargout > 1
 b = g(c,d) ;
end
end

[Walter Roberson]

% code
syms param1 param2
param=[param1;param2];
f3 =((191352748222723/(7128637342969177/1125899906842624)^((param1 - 1)/param1)/(7128637342969177/1125899906842624)^(1/param1))/9511602413006487552 + ((2733703199318633/70368744177664 - param2)^(1 - param1)*(2733703199318633/70368744177664 - param2)^param1)/(561*(param2 - 2733703199318633/70368744177664)))^2 + (log(2733703199318633/70368744177664 - param2)/561 + 2074186557694359/(1125899906842624*param1) - log(-(param2 - 2733703199318633/70368744177664)*(2733703199318633/70368744177664 - param2)^param1)/(2733703199318633/70368744177664 - param2)^param1)^2;
f = matlabFunction(f3,'vars',{param});
gradf3 = jacobian(f3,param).';
gradfh = matlabFunction(gradf3,'vars',{param});
hessf3 = jacobian(gradf3,param);
hessfh = matlabFunction(hessf3,'vars',{param});
low_b = zeros(size(param));
param0=[3.6;2.6];
options = optimoptions('fmincon', ...
  'Algorithm','interior-point', ...   
  'DerivativeCheck', 'on',...   
  'GradObj', 'on',...
  'HessFcn', hessfh, ...
[xfinal,fval,exitflag,output] = fmincon(@(params) oneOrTwo(params, f,gradfh), param0, [], [], [], [], low_b, [], [], options);

% code
function [fun_val, grad_val] = oneOrTwo(params, fun_h, grad_h) 
  fun_val = fun_h(params);
  if nargout > 1
   grad_val = grad_h(params) ;
  end

[Ekin Ceyda Cetin]

I should have done it with three inputs in the function handle, I see now. Thank you for the answers.

[Rustem Devletov]

Hello, friend. I'm really really feeling despondent. I don't know how to implement the following idea. My supervisor told me to supple the gradient to a function from another file. How can I implement this? Can you suggest anything?

[Walter Roberson]

Someone answered you at https://www.mathworks.com/matlabcentral/answers/458884-separate-fmincon-and-gradient#answer_372564