Mathematical Programming

, Volume 136, Issue 1, pp 209–227 | Cite as

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
Full Length Paper Series B

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.

Keywords

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

Mathematics Subject Classification

49M05 49M15 49M37 65F10 65K05 65N22 90C06 90C26 90C30 90C51 90C90 

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Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  • Frank E. Curtis
    • 1
  • Johannes Huber
    • 2
  • Olaf Schenk
    • 3
  • Andreas Wächter
    • 4
  1. 1.Department of Industrial and Systems EngineeringLehigh UniversityBethlehemUSA
  2. 2.Department of Mathematics and Computer ScienceUniversity of BaselBaselSwitzerland
  3. 3.Institute of Computational ScienceUniversitá della Svizzera italianaLuganoSwitzerland
  4. 4.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanstonUSA

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