© 2022, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.In this study, an adjoint based aerodynamic shape optimization of an intake duct is performed for a set of objectives. The objectives include the minimization of total pressure loss, the minimization of total pressure loss constrained with the minimum mass flow rate and the maximization of mass flow rate. M2129 intake duct is taken as the baseline geometry. The Flow and the adjoint solutions are obtained with the open source SU2 software. Optimum configurations provide a significant increase in the total pressure recovery and better distortion characteristics compared to the baseline configuration. The optimum configurations, in general, have similar characteristics in terms of streamwise area distribution and the cross sectional shapes. It is also shown that the radial pressure gradient around the first bend is minimized as a result of high diffusion rates. In addition, the minimization of the total pressure loss results in an unexpected relation between the mass flow rate and the total pressure recovery, which is discussed in detail.