Large-scale aerodynamic and multidisciplinary design problems challenge conventional optimization algorithms, because these problems typically involve thousands of design variables and constraints. Alternative algorithms must be developed that produce solutions to large-scale design problems in a reasonable time. To this end, we investigate a scalable reduced-space Newton–Krylov optimization algorithm. This inexact-Newton algorithm uses a novel matrix-free Krylov solver that requires only KKT-matrix-vector products; these products are formed by solving two linear PDEs. We present preliminary results that benchmark the inexact-Newton algorithm against a conventional quasi-Newton algorithm on the Euler-based drag minimization of the Common-Research-Model wing benchmark. For this problem, the preliminary results indicate that the inexact-Newton algorithm scales well and outperforms the conventional algorithm for problems with more than 500 design variables.