Data Entry: Please note that the research database will be replaced by UNIverse by the end of October 2023. Please enter your data into the system https://universe-intern.unibas.ch. Thanks
An interior-point algorithm for large-scale nonlinear optimization with inexact step computations
Journal
SIAM journal on scientific computing
Volume
32
Number
6
Pages / Article-Number
3447-3475
Keywords
large-scale optimization, constrained optimization, interior-point methods, nonconvex optimization, trust regions, inexact linear system solvers, Krylov subspace methods
Abstract
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 ̈chter [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.
