  Entropy-conservative numerical flux functions can be used to construct
high-order, entropy-stable discretizations of the Euler and Navier-Stokes
equations. The purpose of this short communication is to present a novel family
of such entropy-conservative flux functions. The proposed flux functions are
solutions to quadratic optimization problems and admit closed-form,
computationally affordable expressions. We establish the properties of the flux
functions including their continuous differentiability, which is necessary for
high-order discretizations.
