Constrained Minimization of a Quadratic Form

Question

I am formulating and solving an optimization problem in which the objective function seems to be in the form of $\mathbf{x}^T\mathbf{O}\mathbf{x}$. If it were an unconstrained optimization the minimizer of this objective function would have been an eigenvector of $\mathbf{O}$ corresponding to the smallest eigenvalue. However, this would not work for my case for two reasons, 1) the minimum eigenvalue is negative and that is not acceptable, and 2) the norm of $\mathbf{x}$ is to be bounded by a linear constraint in the form of $\boldsymbol{\rho}^T\mathbf{x}\leq m$. The matrix $\mathbf{O}$ is highly asymmetrical and in square shape. Does anyone have any idea for producing an elegant algebraic formulation or a solution procedure to this problem as a generalized eigen-decomposition problem?