Consider a minimization problem of a convex quadratic function of several variables over a set of inequality constraints of the same type of function. The dual program is a maximization problem with a concave objective function and a set of constraints that are essentially linear. However, the objective function is not differentiable over the constraint region. We study a general theory of dual perturbations and derive a fundamental relationship between a perturbed dual program and the original problem. Based on this relationship, we establish a perturbation theory to display that a well-controlled perturbation on the dual program can overcome the nondifferentiability issue and generate an \(\epsilon\)-optimal dual solution for an arbitrarily small number \(\epsilon\). A simple linear program is then constructed to make an easy conversion from the dual solution to a corresponding \(\epsilon\)-optimal primal solution. Moreover, a numerical example is included to illustrate the potential of this controlled perturbation scheme.