Milan Hladík, Lubomir Kolev, and Iwona Skalna. Sufficient conditions for pseudoconvexity by using linear interval parametric techniques. In Procedings LeGO 2018 - 14th International Global Optimization Workshop, pp. 020001–1--020001-4, AIP Conference Proceedings 2070, American Institute of Physics (AIP), Melville, New York, 2019.
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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 linear interval parametric enclosures of the gradient and the Hessian. It is shown that the new approach results in more efficient tests for checking pseudoconvexity.
@InProceedings{HlaKol2019a,
author = "Milan Hlad\'{\i}k and Lubomir Kolev and Iwona Skalna",
editor = "Michael T. M. Emmerich and others",
feditor = "Michael T. M. Emmerich and Andr\'{e} H. Deutz and Sander C. Hille and Yaroslav D. Sergeyev",
title = "Sufficient conditions for pseudoconvexity by using linear interval parametric techniques",
booktitle = "Procedings {LeGO} 2018 - 14th International Global Optimization Workshop",
series = "AIP Conference Proceedings",
volume = "2070",
number = "1",
publisher = "American Institute of Physics (AIP)",
address = "Melville, New York",
pages = "020001-1--020001-4",
year = "2019",
doi = "10.1063/1.5089968",
isbn = "978-0-7354-1798-4",
issn = "0094-243X",
url = "https://aip.scitation.org/doi/abs/10.1063/1.5089968",
bib2html_dl_html = "https://doi.org/10.1063/1.5089968",
bib2html_dl_pdf = "https://aip.scitation.org/doi/pdf/10.1063/1.5089968",
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 linear interval parametric enclosures of the gradient and the Hessian. It is shown that the new approach results in more efficient tests for checking pseudoconvexity.",
keywords = "Global optimization; Pseudoconvexity; Interval computation; Linear interval parametric enclosures",
}
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