Real roots of real cubics and optimization

The solution of the cubic equation has a century-long history; however, the usual presentation is geared towards applications in algebra and is somewhat inconvenient to use in optimization where frequently the main interest lies in real roots. In this note, we present the roots of the cubic in a for...

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Bibliographic Details
Published inarXiv.org
Main Authors Bauschke, Heinz H, Lal, Manish Krishan, Wang, Xianfu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.02.2023
Subjects
Cubic equations
Optimization
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Summary:The solution of the cubic equation has a century-long history; however, the usual presentation is geared towards applications in algebra and is somewhat inconvenient to use in optimization where frequently the main interest lies in real roots. In this note, we present the roots of the cubic in a form that makes them convenient to use and we also focus on information on the location of the real roots. Armed with this, we provide several applications in optimization where we compute Fenchel conjugates, proximal mappings and projections.
ISSN:2331-8422