An active set method for bound-constrained optimization

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2024
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Neumaier, Arnold
Kimiaei, Morteza
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https://doi.org/10.1080/10556788.2024.2339215
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Austrian Science Fund (FWF): P 34317
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Optimization Methods and Software. Taylor & Francis. ISSN 1055-6788. eISSN 1029-4937. Available under: doi: 10.1080/10556788.2024.2339215
Zusammenfassung

In this article, a class of algorithms is developed for bound-constrained optimization. The new scheme uses the gradient-free line search along bent search paths. Unlike traditional algorithms for bound-constrained optimization, our algorithm ensures that the reduced gradient becomes arbitrarily small. It is also proved that all strongly active variables are found and fixed after finitely many iterations. A Matlab implementation of a bound-constrained solver LMBOPT based on the new theory was discussed by the present authors in a companion paper (Math. Program. Comput. 14 (2022), 271–318).

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Fachgebiet (DDC)
510 Mathematik
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Bound-constrainedoptimization, active setstrategy, line search method, global convergence
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ISO 690NEUMAIER, Arnold, Behzad AZMI, Morteza KIMIAEI, 2024. An active set method for bound-constrained optimization. In: Optimization Methods and Software. Taylor & Francis. ISSN 1055-6788. eISSN 1029-4937. Available under: doi: 10.1080/10556788.2024.2339215
BibTex
@article{Neumaier2024activ-69949,
  year={2024},
  doi={10.1080/10556788.2024.2339215},
  title={An active set method for bound-constrained optimization},
  issn={1055-6788},
  journal={Optimization Methods and Software},
  author={Neumaier, Arnold and Azmi, Behzad and Kimiaei, Morteza}
}
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