Sum of squares generalizations for conic sets
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 10, 2022
- Source ID
- 10.1007/s10107-022-01831-6
Entities
People
- Chris Coey
- Juan Pablo Vielma
- Lea Kapelevich
Organizations
- National Science Foundation
- Office of Naval Research