A note on the implementation of an interior-point algorithm for nonlinear optimization with inexact step computations

Frank E. Curtis, Johannes Huber, Olaf Schenk, Andreas Wächter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis et al. (SIAM J Sci Comput 32:3447-3475, 2010), a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in order to save computational expense. The implementation follows the proposed algorithm, but includes many practical enhancements, such as functionality to avoid the computation of a normal step during every iteration. The implementation is included in the IPOPT software package paired with an iterative linear system solver and preconditioner provided in PARDISO. Numerical results on a large nonlinear optimization test set and two PDE-constrained optimization problems with control and state constraints are presented to illustrate that the implementation is robust and efficient for large-scale applications.

Original languageEnglish (US)
Pages (from-to)209-227
Number of pages19
JournalMathematical Programming
Volume136
Issue number1
DOIs
StatePublished - Dec 2012

Keywords

  • Inexact linear system solvers
  • Interior-point methods
  • Krylov subspace methods
  • Large-scale optimization
  • Line search
  • Nonconvex programming
  • PDE-constrained optimization
  • Trust regions

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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