Trying to solve system $(A+\lambda{W})x=b$ (derived from the method of Lagrange multipliers) where $\lambda \in \mathbb{R}$ - the Lagrange multiplier. $A$ - symmetric non-singular matrix. $W$ - square diagonal matrix such $W = P+P^T$.
Primary goal is minimize $\|Fx-g\|^2$ s.t. $x^TPx=c$
I found papper "Eigenvalue and Generalized Eigenvalue Problems: Tutorial" where provided solution for $(A+\lambda{W})x=\textbf{0}$ and called "generalized eigenvalue problem".
Other way for possible solution - write a problem as system of polynomials (in my case it will be system 10 equations of 2th degree polynomials with 10 unknowns) but matlab can't solve it.
Any suggestions about solution?