Constrained Optimization, a function that returns a vector?

Hello! I looking for some matlab function (Constrained Optimization) which one returns a vector. The function what I try minimalize is in the attachment. It is MPC problem. I try to solve some problem like:

 A = [];
 b = [];
 x0 = [0,0,0]

 fun = @(x)(([3;3;3]-[3;3;3])'*([3;3;3]-[3;3;3])+parameter*(x-[1;1;1])'*(x-[1;1;1]))

 [x,fval] = optimalization_function(fun,x0,A,b)

Matrices like [3;3;3] is just example.

I tried 'fmincon' but it works only for function that returns scalar.

Answer 1

[Alan Weiss]

What does minimizing a vector mean? it doesn't mean anything mathematically. You cannot minimize a vector.

The equation in your attached image minimizes the NORM of a vector. That is a scalar, and makes sense to minimize. If you as fmincon to minimize the norm of a vector function, it will happily attempt to do so.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[jaskier222]

Hmm, I used:

x0=[0,0,0]  
A=[]
b=[]
  [x,fval] = fmincon(fun,x0,A,b) 
fun = @(x)((y_zad_k-y_k)'*(y_zad_k-y_k)+parameter*(x-u_k_1)'*(x-u_k_1))

where 
N = 6;
N_u = 3;
y_zad is matrix [Nx1]
y_k is matrix [Nx1]
u_k_1 is matrix [N_ux1]

matlab gave me this: "Supplied objective function must return a scalar value." All I placed id 2-level matlab function.

[Alan Weiss]

Evaluate fun(x0). If you don't get a scalar, then your function is not scalar-valued. If you do get a scalar, then please ask again.

Alan Weiss

MATLAB mathematical toolbox documentation

[Alan Weiss]

I just had another idea. Try

x0 = zeros(3,1);

I think that your original x0 is a row vector, but should be a column vector.

Alan Weiss

MATLAB mathematical toolbox documentation