Minimization of an Non linear objective function that is product of matrix variables and known matrixes.

I have a non linear optimization problem with two matrices as variables. The objective funciton is product of these variables and some known matrices. The objective function is of the following form: min (AY+(I-AB)H-X)' * (AY+(I-AB)H-X) s.t (I-BA)Y=0 where A=C+K-CBKBC.

Note that only K and H are unknown matrices, all others are known matrices.

Can some one please help me out in writing this optimization problem using fmincon.

[Torsten]

Can you give the dimension of AY+(I-AB)H-X ?

[Bala]

Dimensions of AY+(I-AB)H-X is 121 X 1.

A -> (121 X 28) Y -> (28 X 1) I -> (121 X 121) A -> (121 X 28) B -> (28 X 121) H -> (121 X 1) X -> (121 X 1)

[Torsten]

I->(121x121), B*A->(28x28). Thus I-B*A is not defined.

[Awnish Kumar]

I is an identity matrix. In the term (I-AB), the dimension of I is (121 X 121). And in the term (I - BA), the dimension of I is (28 X 28).

[Torsten]

As stated, you have 29*121 free parameters to be adjusted. Such an optimization will never be successful if blindly performed. Of course, you could create a vector of length 3509 where the first 3388 elements form the matrix K and the last 121 elements form the vector H, define the objective function and the function for the nonlinear constraints and let fmincon start. But this will lead to nothing.

You should study the literature for the background of your problem and extract the specific numerical methods on how it is solved.

Best wishes

Torsten.