Let us assume I have to optimize this system:
$$\min_{x\in S} \left|\left|\left(E\begin{bmatrix} I_n\\ A'(x)^{-1}C'(x)\\ \end{bmatrix}\right)^+ a -b\right|\right|^{2}$$
Where x is the vector of my unknowns, A', B' are matrices depending on x while a and b are constant vectors with correct dimensions and E is a matrix with correct dimensions too. S are the constaints on my x variables which are simple linear inequalities.
Which is the best approach in order to solve this problem? Suggestions? How to handle both pseudo inverse and inverse?