fminsearch error: DOUBLE cannot convert the input expression into a double array - matlab

Question

I am encountering a problem during an optimization exercise. I am trying to use fminsearch() in matlab to solve it. The following error is generated when the code is run:
The following error occurred converting from sym to double: Error
using symengine (line 59) DOUBLE cannot convert the input expression
into a double array. If the input expression contains a symbolic
variable, use VPA.
Error in fminsearch (line 190) fv(:,1) = funfcn(x,varargin{:});
Error in Optimization (line 22) sol2 = fminsearch(J, x0);
The script I use can be seen below. The f is the minimization problem where g1 & g2 are constraints. The p is there so that I can turn it into for loop later.
syms x1 x2 x3 x4;
syms p;
f = x1.^4 - x3.^2 + x1*x3 + x2*x4 - 5*x2 + 3;
g1 = x1.^2 + x2.^2 + x3.^2 + x4.^2 - 1;
g2 = x1 + x3 - 1;
x0 = [2 2 2 2];
p = 3;
J = #(x1,x2,x3,x4) sym(f + p * g1.^2 + g2.^2);
sol2 = fminsearch(J, x0);
This Stackoverflowpost has the same problem but in another perspective.According to this post it might be a problem with allocating the in a valid way. I tried a few different ways to solve my problem. I have tried matlabFunction() and putting the function in a seperate file.
If the input expression contains a symbolic variable, use the VPA function instead?
Thanks in advance for the help.

Answer 1

fminsearch is designed for numerical minimization. There is little point in using symbolic math in this case (it can be used, but it will be slower, complicate your code, and the results will still be in double precison). Second, if you read the documentation and look at the examples for fminsearch, you'll see that it requires a function that takes a single vector input (as opposed to four scalars in your case). Here's how you could rewrite your equations using anonymous functions:
f = #(x)x(1).^4 - x(3).^2 + x(1).*x(3) + x(2).*x(4) - 5*x(2) + 3;
g1 = #(x)x(1).^2 + x(2).^2 + x(3).^2 + x(4).^2 - 1;
g2 = #(x)x(1) + x(3) - 1;
x0 = [2 2 2 2];
p = 3;
J = #(x)f(x) + p*g1(x).^2 + g2(x).^2;
sol2 = fminsearch(J, x0)
this returns
sol2 =
0.149070165097281 1.101372214292880 0.326920462283209 -0.231885482601008
Using symbolic math and subs:
syms x1 x2 x3 x4;
f = x1^4 - x3^2 + x1*x3 + x2*x4 - 5*x2 + 3;
g1 = x1^2 + x2^2 + x3^2 + x4^2 - 1;
g2 = x1 + x3 - 1;
x0 = [2 2 2 2];
p = sym(3);
J = #(X)subs(f + p*g1^2 + g2^2,[x1 x2 x3 x4],X);
sol2 = fminsearch(J, x0)
which returns identical results.