fmincon optimize matrices of different size

Ciao everyone.

I am trying to use fmincon for an optimization task. And I am not sure if fmincon can do this.

For an easy example:

There is a matrix x1 (size 3*3), and there is another matrix x2(size 4*4)

The objective function is

fun = A1*(x1-A)^2*A1'+ B1*(x2-B)^2*B1'

size of A1 is 1*3

A is 3*3

B1 is 1*4

B is 4*4

so we get objective function as a scalar.

The normal approach is to reshape the x1 and x2 and put them into a single vector x for optimization.

My question is that is there a way to formulate the x as x = [x1, x2] directly as matrices of different sizes?

Answer 1

[Matt J]

x1=optimvar('x1',3,3);
x2=optimvar('x2',4,4);

fun = fcn2optimexpr(  @(x1,x2) A1*(x1-A)^2*A1'+ B1*(x2-B)^2*B1'   ,x1,x2)

p=optimproblem('Objective',fun);

sol=solve(p)

[Jing Xie]

Thanks a lot! That works!