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AERODYNAMIC Shape Optimization (ASO) us-ing gradient based optimization methods typically requires gradients with respect to a large number of design variables. Traditional methods of computing these gradients, such as finite differencing, are computationally unfeasible for realistic problems. However, the computational cost can be significantly decreased through the use of an adjoint equation. The adjoint method yields the gradient with respect to an arbitrary number of design variables for the cost of a single flow solution and a single adjoint solution. 1" 3 The application of the adjoint has produced remarkable improvements in the ability to design for certain types of optimal behavior, but it is not possible, in general, to treat arbitrary cost functions. Application in multidisciplinary design work is thus limited and often requires artificial constraints to account for other disciplines. For example, in the case of wing …