How to compute cost function for fmincon?

Hi all, I'm performing an optimization using fmincon as follows:

r=[0.22 9.94 0.08;
   0.16 0.95 0.08;
   0.07 0.87 0.08];
R = [0.49; 0.42; 0.19];

x = fmincon(@(x) norm(r*x-R)^2, ones(3,1)/3, [], [], ones(1,3), 1, zeros(3,1), []);

Here, I wan to use a cost function for this optimization.

where , and x is a vector of initial guess values.

Could you somebody help me with this?

[Matt J]

The cost function you have shown is vector-valued. Do you mean to minimize its Euclidean norm?

Answer 1

[Matt J]

r=[0.22 9.94 0.08;
   0.16 0.95 0.08;
   0.07 0.87 0.08];
R = [0.49; 0.42; 0.19];

omega=0.1;
gamma=150;
fun=@(x) norm(    (r*x-R) + omega*(1-tanh(x*gamma)-gamma*tanh(x-1) )     )^2 ;

x = fmincon(@(x) fun, ones(3,1)/3, [], [], ones(1,3), 1, zeros(3,1), []);

[hinami]

Thanks, Matt, but I got an error:

"Error using fmincon (line 710)

FMINCON requires all values returned by functions to be of data type double."

How can I solve this error?

[Matt J]

Running this test,

clear

r=[0.22 9.94 0.08;
   0.16 0.95 0.08;
   0.07 0.87 0.08];
R = [0.49; 0.42; 0.19];
omega=0.1;
gamma=150;
fun=@(x) norm(    (r*x-R) + omega*(1-tanh(x*gamma)-gamma*tanh(x-1) )     )^2 ;

funx0=fun(ones(3,1)/3)

should give the result,

funx0 =

  291.1478

[hinami]

Yes, this works fine.

[hinami]

Now it works fine with

r=[0.22 9.94 0.08;
   0.16 0.95 0.08;
   0.07 0.87 0.08];
R = [0.49; 0.42; 0.19]
omega=0.1;
gamma=150;
x = fmincon(@(x) norm(  r*x-R  +  omega*(1-tanh(x*gamma)-tanh((x-1)*gamma))  )^2, ones(3,1)/3, [], [], ones(1,3), 1, zeros(3,1), []);