The theoretical development and implementation of an optimization technique based on optimal control method is presented for the two-dimensional full-potential flow model. This technique, in comparison with the classical finite-differences approach (brute force), provides major savings in the overall computational cost. The reduction on computational effort is due to the fact that the gradient of a cost function can be evaluated by a closed form equation after the solution of an adjoint equation. Since this adjoint equation is similar to the full-potential equation itself, the same solution algorithm is applied. Inverse design problems are solved using optimization in both subsonic and transonic flows. Also wave drag minimization is successfully accomplished.