Alldredge, Graham WestKinetic equations are used to model many physical phenomena, including gas dynamics, semiconductors, radiative transport, and more. However, high dimensionality of the domain of definition of the system makes simulation difficult. The entropy-based moment closure model of the kinetic equation reduces the dimension of the domain and has attractive theoretical and practical properties, but most implementations have avoided numerically solving the defining optimization problem. We use the linear one-dimensional slab-geometry model to expose the main challenges in the use of numerical optimization then propose an isotropic regularization and describe the benefits of using fixed quadrature. A numerical technique using adaptive polynomial bases in the optimization algorithm is also tested. We develop manufactured solutions to test our algorithm and also present its performance on two standard test problems.DissertationElectrical engineering