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

Frank E. Curtis, Olaf Schenk, Andreas Wächter

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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 Wächter [SIAM J. Optim., 20 (2009), pp. 1224-1249], with additional functionality for handling nequality 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 PDEconstrained model problems.

Original languageEnglish (US)
Pages (from-to)3447-3475
Number of pages29
JournalSIAM Journal on Scientific Computing
Volume32
Issue number6
DOIs
StatePublished - Dec 1 2010

Keywords

  • Constrained optimization
  • Inexact linear system solvers
  • Interior-point methods
  • Krylov subspace methods
  • Large-scale optimization
  • Nonconvex optimization
  • Trust regions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'An interior-point algorithm for large-scale nonlinear optimization with inexact step computations'. Together they form a unique fingerprint.

Cite this