Milan Hladík. Testing pseudoconvexity via interval computation. J. Glob. Optim., 71(3):443–455, 2018.
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We study the problem of checking pseudoconvexity of a twice differentiable function on an interval domain. Based on several characterizations of pseudoconvexity of a real function, we propose sufficient conditions for verifying pseudoconvexity on a domain formed by a Cartesian product of real intervals. We carried out numerical experiments to show which methods perform well from two perspectives - the computational complexity and effectiveness of recognizing pseudoconvexity.
@article{Hla2018c,
author = "Milan Hlad\'{\i}k",
title = "Testing pseudoconvexity via interval computation",
journal = "J. Glob. Optim.",
fjournal = "Journal of Global Optimization",
volume = "71",
number = "3",
pages = "443-455",
year = "2018",
doi = "10.1007/s10898-017-0537-6",
issn = "0925-5001",
bib2html_dl_html = "http://dx.doi.org/10.1007/s10898-017-0537-6",
bib2html_dl_pdf = "http://rdcu.be/s1KE",
abstract = "We study the problem of checking pseudoconvexity of a twice differentiable function on an interval domain. Based on several characterizations of pseudoconvexity of a real function, we propose sufficient conditions for verifying pseudoconvexity on a domain formed by a Cartesian product of real intervals. We carried out numerical experiments to show which methods perform well from two perspectives - the computational complexity and effectiveness of recognizing pseudoconvexity.",
keywords = "Global optimization; Interval computation; Pseudoconvexity",
}
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