The authors consider the use of preconditioned iterative linear solvers to solve large-scale nonlinear optimization problems. One way to handle nonconvexity and generate search directions that promote convergence to local minimizers is to ensure a specific inertia of the saddle point matrix used in the computation of optimization steps. The authors examined the effectiveness of a new preconditioner for nonconvex problems. At the heart of the preconditioner lies the use of symmetric matchings on each level, and in the preconditioning stage lies the use of the inertia-revealing, inverse-based, and eigenvalue-bounded incomplete factorization preconditioner. The method is able to reveal the inertia of the original matrix sufficiently accurately. It is reliable and robust enough to allow a general-purpose interior point optimization code to solve a large variety of nonlinear nonconvex optimization problems. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale three-dimensional (3D) PDE-constrained optimal control problems, and on 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with \(150^3\) state variables and \(150^2\) control variables, both subject to bound constraints.