Steklov regularization and trajectory methods for univariate global optimization

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buir.contributor.authorArıkan, Orhan
buir.contributor.orcidArıkan, Orhan|0000-0002-3698-8888
dc.citation.epage120en_US
dc.citation.issueNumber1en_US
dc.citation.spage91en_US
dc.citation.volumeNumber76en_US
dc.contributor.authorArıkan, Orhan
dc.contributor.authorBurachik, R. S.
dc.contributor.authorKaya, C. Y.
dc.date.accessioned2021-02-19T08:34:27Z
dc.date.available2021-02-19T08:34:27Z
dc.date.issued2020
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe introduce a new regularization technique, using what we refer to as the Steklov regularization function, and apply this technique to devise an algorithm that computes a global minimizer of univariate coercive functions. First, we show that the Steklov regularization convexifies a given univariate coercive function. Then, by using the regularization parameter as the independent variable, a trajectory is constructed on the surface generated by the Steklov function. For monic quartic polynomials, we prove that this trajectory does generate a global minimizer. In the process, we derive some properties of quartic polynomials. Comparisons are made with a previous approach which uses a quadratic regularization function. We carry out numerical experiments to illustrate the working of the new method on polynomials of various degree as well as a non-polynomial function.en_US
dc.identifier.doi10.1007/s10898-019-00837-3en_US
dc.identifier.issn0925-5001
dc.identifier.urihttp://hdl.handle.net/11693/75476
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttps://dx.doi.org/10.1007/s10898-019-00837-3en_US
dc.source.titleJournal of Global Optimizationen_US
dc.subjectGlobal optimizationen_US
dc.subjectMean filteren_US
dc.subjectSteklov smoothingen_US
dc.subjectSteklov regularizationen_US
dc.subjectScale–shift invarianceen_US
dc.subjectTrajectory methodsen_US
dc.titleSteklov regularization and trajectory methods for univariate global optimizationen_US
dc.typeArticleen_US

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