An optimal control methodology is applied to the problem of finding the heat, hydrogen, and oxygen flux profiles for the homogeneous, gas-phase conversion of methane to ethylene in a plug flow reactor. The calculations use a detailed reaction model for the oxidative pyrolysis of methane and a model for the growth of polycyclic aromatic hydrocarbons and soot:particle nulceation and growth. The reactor designs show that distributed hydrogen and oxygen fluxes along the axis of the reactor improve ethylene yields to a greater extent than co-fed hydrogen and/or oxygen. The axial heat flux is shown to play a major role in the final yields of ethylene. The optimal residence times are 28-31 ms, and the optimal temperature profiles cover a range of 1200-1985 K. The simulation results show that for the conditions considered, C2H2 is formed initially and is converted to C2H4 by a controlled extraction of energy. Hydrogen addition is advantageous at both stages to reduce soot in the first half of the reactor and to shift the equilibrium toward ethylene in the second half. Oxygen aids in forming ethylene from the C2H5 and C2H3 intermediates and in the formation of hydrogen radicals. Ethylene carbon mass fractions of 0.64 have been achieved. The solutions, although not proven to be globally optimal, are of high quality.