  We present a new entropy-based moment method for the velocity discretization
of kinetic equations. This method is based on a regularization of the
optimization problem defining the original entropy-based moment method, and
this gives the new method the advantage that the moment vectors of the solution
do not have to take on realizable values. We show that this equation still
retains many of the properties of the original equations, including
hyperbolicity, an entropy-dissipation law, and rotational invariance. The cost
of the regularization is mismatch between the moment vector of the solution and
that of the ansatz returned by the regularized optimization problem. However,
we show how to control this error using the parameter defining the
regularization. This suggests that with proper choice of the regularization
parameter, the new method can be used to generate accurate solutions of the
original entropy-based moment method, and we confirm this with numerical
simulations.
