Sum of squares generalizations for conic sets
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10107_2022_Article_1831.pdf
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Author(s)
Kapelevich, Lea
Coey, Chris
Vielma, Juan Pablo
Date Issued
June 2022
Journal
Mathematical Programming
Publisher
Springer Science and Business Media LLC
Citation
Kapelevich, Lea, Coey, Chris and Vielma, Juan P. 2022. "Sum of squares generalizations for conic sets."
Version
Final published version
Abstract
Abstract
Polynomial nonnegativity constraints can often be handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and Yildiz (Papp D in SIAM J O 29: 822–851, 2019), using the sum of squares cone directly in an interior point algorithm. Beyond nonnegativity, more complicated polynomial constraints (in particular, generalizations of the positive semidefinite, second order and
$$\ell _1$$
ℓ
1
-norm cones) can also be modeled through structured sum of squares programs. We take a different approach and propose using more specialized cones instead. This can result in lower dimensional formulations, more efficient oracles for interior point methods, or self-concordant barriers with smaller parameters.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10107-022-01831-6
