Low-altitude windshear is a threat to the safety of aircraft in take-off and landing: over the past 20 years, some 30 aircraft accidents have been attributed to windshear. The Aero-Astronautics Group of Rice University under the direction of Dr. Angelo Miele has determined the optimal capability of an aircraft in take-off under windshear conditions and has developed near-optimal guidance strategies. In this thesis, using the above information, the values of the parameters for different guidance strategies are determined in order to provide the best approximation to the optimal capabilities. The calculation is treated as a mathematical programming problem, solved by the Nelder-Mead simplex algorithm. Then, the optimal parameters data are applied to guidance strategies. The resulting guidance trajectories are presented in graphical form along with the optimal trajectories for comparison.