How to use fminsearch with a symbolic function with a variable number of symbols?

Hello Matlab community,

I am struggling with an optimization problem for which I want to use the function fminsearch. The following example is as minimized as possible. I want to have a variable number of parameters and the splitting of the function "funfun" into "fun1" and "fun2" is necessary. The resulting function in this example is the Rosenbrock's function from the fminsearch documentation page ( fminsearch ). I am using Matlab 2014a.

numPar = 2;
a = sym('a', [1 numPar]);
fun1 = symfun(100*(a(2)-a(1)^2)^2, a);
fun2 = symfun((1-a(1))^2, a);
funfun = fun1 + fun2
a0 = [-1.2, 1];
fminsearch(funfun,a0)

This code runs into the error:

Error using symfun/subsref (line 135)
Symbolic function expected 2 inputs and received 1.

Error in fminsearch (line 190)
fv(:,1) = funfcn(x,varargin{:});

Thanks for your help in advance! Cheers

Answer 1

[Alan Weiss]

Before running fminsearch, convert your symbolic expression to a MATLAB function by using matlabFunction:

myfun = matlabFunction(funfun,'Vars',{a});
a0 = [-1,1];
[x,fval,exitflag,output] = fminsearch(myfun,a0)

When I ran this I got the following result:

x =

      1.0000    1.0000

fval =

     4.0576e-10

exitflag =

       1

output = 

    struct with fields:

      iterations: 100
       funcCount: 187
       algorithm: 'Nelder-Mead simplex direct search'
         message: 'Optimization terminated:↵ the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 ↵ and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-04 ↵'

Alan Weiss

MATLAB mathematical toolbox documentation

[Benjamin]

Hi Alan, thank you very much for your help. This works perfect.

[Lukasz Grzybowski]

What if it would be function of two parameters?

[Alan Weiss]

The example IS a function of two parameters, x(1) and x(2). Just combine your parameters into the same vector, x.

Alan Weiss

MATLAB mathematical toolbox documentation