We present a line-search algorithm for large-scale continuous optimization. The algorithm 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 save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact Newton method for equality constrained optimization proposed by Curtis, Nocedal, and W¨achter [SIAM J. Optim., 20 (2009), pp. 1224–1249], with additional functionality for handling inequality 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.
F. E. Curtis, O. Schenk, and A. W¨achter, “An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations,” SIAM Journal on Scientific Computing, 32(6): 3447–3475, 2010.