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Linear interval parametric approach to testing pseudoconvexity

Author

Listed:
  • Milan Hladík

    (Charles University)

  • Lubomir V. Kolev

    (Technical University of Sofia)

  • Iwona Skalna

    (AGH University of Science and Technology)

Abstract

The recent paper ( DOI: 10.1007/s10898-017-0537-6 ) suggests various practical tests (sufficient conditions) for checking pseudoconvexity of a twice differentiable function on an interval domain. The tests were implemented using interval extensions of the gradient and the Hessian of the function considered. In this paper, we present an alternative approach which is based on the use of more accurate affine form enclosures and affine arithmetic. We modify the tests to work with linear interval parametric enclosures of the gradients and the Hessians. We also present computational complexity results, showing that performing some tests exactly is NP-hard. It is shown by numerical experiments on random and benchmark data that the new approach results in more efficient tests for checking pseudoconvexity, however, at the expense of higher computation time.

Suggested Citation

  • Milan Hladík & Lubomir V. Kolev & Iwona Skalna, 2021. "Linear interval parametric approach to testing pseudoconvexity," Journal of Global Optimization, Springer, vol. 79(2), pages 351-368, February.
  • Handle: RePEc:spr:jglopt:v:79:y:2021:i:2:d:10.1007_s10898-020-00924-w
    DOI: 10.1007/s10898-020-00924-w
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    References listed on IDEAS

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    1. Eligius M.T. Hendrix & Boglárka G.-Tóth, 2010. "Introduction to Nonlinear and Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-88670-1, September.
    2. Anders Skjäl & Tapio Westerlund, 2014. "New methods for calculating $$\alpha $$ BB-type underestimators," Journal of Global Optimization, Springer, vol. 58(3), pages 411-427, March.
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