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- Title
Sum of squares generalizations for conic sets.
- Authors
Kapelevich, Lea; Coey, Chris; Vielma, Juan Pablo
- 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 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.
- Subjects
THAILAND; SUM of squares; INTERIOR-point methods; SEMIDEFINITE programming; GENERALIZATION; HERMITIAN forms; CONIC sections
- Publication
Mathematical Programming, 2023, Vol 199, Issue 1/2, p1417
- ISSN
0025-5610
- Publication type
Article
- DOI
10.1007/s10107-022-01831-6