<p>Simulation-based multiphysics and multidisciplinary models are fundamental building blocks of design optimization frameworks that involve coupled systems. One common challenge arises when the coupled linear and nonlinear systems that represent these models result in a saddle-point problem. Such problems require a Newton-type method instead of block Gauss–Seidel based methods because the Jacobian matrix has a non-invertible block. We introduce nonlinear Schur complement and linear Schur complement solvers suitable for solving saddle-point problems. We implement these solvers in NASA’s OpenMDAO framework and demonstrate their effectiveness through two analytic problems and an aerodynamic shape optimization of an aircraft wing. The solvers enable flexible and robust formulation of optimization problems by circumventing the numerical challenges inherent in saddle-point systems. This approach can be applied to a wide range of saddle-point problems in simulation-based optimization, making it particularly valuable for multidisciplinary design applications. </p>