Input clarification for the fmincon function

Hello everyone,

I'm trying to use the fmincon funtion but I'm having some problems with the input of the function.

I have a fairly complicated problem and I'm generating the function to be minimized f(v) by using Matlab symbolic variables in order to calculate the Gradient and the Hessian of this function by using the Symbolic Math Toolbox:

function [f,g,gg]=CostFunction(t,Y,Nvar,Epsilon)
% Symbolic Cost function, Gradient and Hessian
sympref('FloatingPointOutput',true);
Hsym=sym(zeros(length(t),1)).';

for i = 1:Nvar
    v{i} = sprintf('v%d%d',i);
end
v = v(:);
v = sym(v, 'real');

for i = 1:4:Nvar
    Hsym = Hsym+v(i).*exp(-v(i+1).*t).*cos(2.*pi.*v(i+3).*t+v(i+2)); % Impulse Responce Function
end
tic
f_sym = sum((Hsym-Y).^2)-Epsilon; % Cost Function
f=matlabFunction(f_sym);

g_sym = jacobian(f_sym,v).'; % Gradient Function
for i=1:length(g_sym)
    g{i}=matlabFunction(g_sym(i));
end

gg_sym = jacobian(g_sym,v); % Hessian Function
for i=1:length(gg_sym)
    for j=1:length(gg_sym)
        gg{i,j}=matlabFunction(gg_sym(i,j));
    end
end

end

What I get from this code is a function f(v) and a cell array cointining the gradint function g(v) and the hessian function gg(v).

How can I provide these functions to the minimization algorithm fmincon? A possible solution is, as suggested in this link, to use something like:

matlabFunction(f,g,gg,'file',filename,'vars',{v});

but it takes a lot of computational time.

You can find attatched the Workspace for running this script.

Is there another way to use f,g,gg inside fmincon?

Thank you in advance for your help.

Best Regards,

Davide

[Torsten]

A possible solution is, as suggested in this link, to use something like:

matlabFunction(f,g,gg,'file',filename,'vars',{v});

but it takes a lot of computational time.

Do it once, save the expressions to file and for further runs, use the function files instead of the symbolic computations.

[Davide Mastrodicasa]

Thank you for your reply @Torsten.

The problem in this case will be that the Y input of my function changes in a for loop of approximately 1000 vectors so I have to run the symbolic computations multiple times.

What I have to do is just to place the g ang gg in a proper form for fmincon. A rough copy/paste of the function contained in the cell array g and gg should work but I do not know how to make it automatically.

[Walter Roberson]

 matlabFunction(f,g,gg,'file',filename,'vars',{v});

I recommend using 'optim', false when you write to file. There are bugs in the optimization process in recent releases. Not optimizing saves a fair bit of time too.

[Davide Mastrodicasa]

Do you mean 'Optimize',false ?

[Walter Roberson]

yes

[Matt J]

'Optimize',false can be abbreviated to 'optim', false if desired

[Matt J]

Why use the Symbolic Math Toolbox at all? Your function and its derivatives look very easy.

[Davide Mastrodicasa]

My idea was to use Symbolic Math Toolbox to be sure of the correctness of the calculation. I did not think that the computational time was high. I will try to calculate them manually and implement them in the code.

Thank you for your suggestion