Sum of squares generalizations for conic sets

• 成果类型: Article
• 署名作者: Kapelevich, Lea; Coey, Chris; Vielma, Juan Pablo
• 署名单位: Massachusetts Institute of Technology (MIT); Alphabet Inc.; Google Incorporated; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01831-6
• 发表日期: 2023
• 页码: 1417-1429
• 关键词: optimization problems; relaxations; cones

摘要

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.