The individual discipline feasible (IDF) formulation is a modular multidisciplinary design optimization architecture that promotes the use of disparate discipline analysis tools. IDF achieves modularity by introducing coupling variables and coupling constraints into the optimization problem, which enables the state equations for each discipline to be solved independently at each optimization iteration. However, the increased number of optimization variables and nonlinear state-based constraints poses a significant challenge to conventional matrix-explicit optimization algorithms. In this paper, we apply a reduced-space inexact-Newton-Krylov (RSNK) algorithm to a large-scale, high-fidelity aerostructural optimization of a commercial airliner wing. Our findings demonstrate that the RSNK algorithm, paired with a novel matrix-free preconditioner, can solve the IDF problem at least as fast as its multidisciplinary feasible counterpart. In particular, the IDF preconditioner remains highly effective even in the presence of thousands of coupling constraints.