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

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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.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA

    Frank E. Curtis

  2. Department of Mathematics and Computer Science, University of Basel, Basel, Switzerland

    Johannes Huber

  3. Institute of Computational Science, Universitá della Svizzera italiana, Lugano, Switzerland

    Olaf Schenk

  4. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA

    Andreas Wächter

Authors
  1. Frank E. Curtis
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  2. Johannes Huber
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  3. Olaf Schenk
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  4. Andreas Wächter
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Corresponding author

Correspondence to Andreas Wächter.

Additional information

Frank E. Curtis was supported by National Science Foundation grant DMS-1016291.

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Curtis, F.E., Huber, J., Schenk, O. et al. A note on the implementation of an interior-point algorithm for nonlinear optimization with inexact step computations. Math. Program. 136, 209–227 (2012). https://doi.org/10.1007/s10107-012-0557-4

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  • DOI: https://doi.org/10.1007/s10107-012-0557-4

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