  We consider the method-of-moments approach to solve the Boltzmann equation of
rarefied gas dynamics, which results in the following moment-closure problem.
Given a set of moments, find the underlying probability density function. The
moment-closure problem has infinitely many solutions and requires an additional
optimality criterion to single-out a unique solution. Motivated from a
discontinuous Galerkin velocity discretization, we consider an optimality
criterion based upon L2-minimization. To ensure a positive solution to the
moment-closure problem, we enforce positivity constraints on L2-minimization.
This results in a quadratic optimization problem with moments and positivity
constraints. We show that a (Courant-Friedrichs-Lewy) CFL-type condition
ensures both the feasibility of the optimization problem and the L2-stability
of the moment approximation. Numerical experiments showcase the accuracy of our
moment method.
