An interior-point algorithm for large-scale nonlinear optimization with inexact step computations

We present a line-search algorithm for large-scale continuous optimization. Thealgorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead,it uses iterative linear system solvers. Inexact step computations are supported in order to savecomputational expense during each iteration. The algorithm is an interior-point approach derivedfrom an inexact Newton method for equality constrained optimization proposed by Curtis, Nocedal,and W ̈chter [SIAM J. Optim., 20 (2009), pp. 1224–1249], with additional functionality for handlinginequality constraints. The algorithm is shown to be globally convergent under loose assumptions.Numerical results are presented for nonlinear optimization test set collections and a pair of PDE-constrained model problems.