I have a function $f(X) = |a^T X^{-1} a|$ that maps a complex symmetric matrix $X = X^T \neq X^H$ to a real number. I would like to perform optimization involving this function, and I try to convert $f(X)$ to a quadratic form of a Hermitian matrix $g(Y) = b^H Y^{-1} b$, which may be more easy to optimize since the eigenvalues are real. Are there any tricks like increasing the size of matrices that can may help? Thanks.
