How could I solve the following optimization problem using MATLAB or an other way?
Given ${E}^{1}, {A}^{21}, {A}^{22}, {C}^{1}, {A}^{12}$
$ \underset{{C}^{2}, {E}^{2}}{min} {\left \| {C}^{2}{E}^{1} - {A}^{21} \right \|}_{F}^{2} + {\left \| {C}^{2}{E}^{2} - {A}^{22} \right \|}_{F}^{2} + {\left \| {C}^{1}{E}^{2} - {A}^{12} \right \|}_{F}^{2} $
I know the approximated linear solution, assuming $ {A}^{22} $ is negligible is given by:
$ {C}^{2} = {A}^{21} {{E}^{1}}^{T} {\left( {E}^{1} {{E}^{1}}^{T} \right)}^{-1}, {E}^{2} = {\left( {\begin{bmatrix} {C}^{1}\\ {C}^{2} \end{bmatrix}}^{T} \begin{bmatrix} {C}^{1}\\ {C}^{2} \end{bmatrix} \right)}^{-1} {\begin{bmatrix} {C}^{1}\\ {C}^{2} \end{bmatrix}}^{T} \begin{bmatrix} {A}^{12}\\ {A}^{22} \end{bmatrix} $
Yet it would be nice to know how to solve it accurately. Thanks.