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Linear interval parametric approach to testing pseudoconvexity

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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.

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Notes

  1. engine.h is a C/C++ header file for MATLAB engine programs, it contains function prototypes for engine routines.

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Acknowledgements

M. Hladík was supported by the Czech Science Foundation Grant P403-18-04735S.

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Authors and Affiliations

  1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Milan Hladík

  2. Department of Theoretical Electrotechnics, Technical University of Sofia, Sofia, Bulgaria

    Lubomir V. Kolev

  3. AGH University of Science and Technology, Kraków, Poland

    Iwona Skalna

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  1. Milan Hladík
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  2. Lubomir V. Kolev
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  3. Iwona Skalna
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Correspondence to Milan Hladík.

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Hladík, M., Kolev, L.V. & Skalna, I. Linear interval parametric approach to testing pseudoconvexity. J Glob Optim 79, 351–368 (2021). https://doi.org/10.1007/s10898-020-00924-w

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