Semi-definite Representations for Sets of Cubics on the Two-dimensional Sphere

Roland Hildebrand ()
Additional contact information
Roland Hildebrand: Université Grenoble Alpes, CNRS, Grenoble INP, LJK

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 12, 666-675

Abstract: Abstract The compact set of homogeneous quadratic polynomials in n real variables with modulus bounded by 1 on the unit sphere is trivially semi-definite representable. The compact set of homogeneous ternary quartics with modulus bounded by 1 on the unit sphere is also semi-definite representable. This suggests that the compact set of homogeneous ternary cubics with modulus bounded by 1 on the unit sphere is semi-definite representable. We deduce an explicit semi-definite representation of this norm ball. More generally, we provide a semi-definite description of the cone of inhomogeneous ternary cubics which are nonnegative on the unit sphere. This allows to incorporate nonnegativity conditions on polynomials in this space into semi-definite programs by transforming them into semi-definite constraints on the coefficient vector.

Keywords: Nonnegative polynomials; Semi-definite representations; Norm balls; Polynomial optimization; 90C23; 90C22 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-022-02104-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02104-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-022-02104-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().