The problem of estimating the domain of attraction of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities is proposed. Moreover, for the case of odd polynomial systems, a relaxed criterion for obtaining an effective starting candidate of the optimal quadratic Lyapunov function is presented.