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Program."],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Polynomial nonnegativity constraints can often be handled using the <jats:italic>sum of squares<\/jats:italic> 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\u2013851, 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\ell _1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-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.\n<\/jats:p>","DOI":"10.1007\/s10107-022-01831-6","type":"journal-article","created":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T08:24:56Z","timestamp":1654849496000},"page":"1417-1429","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sum of squares generalizations for conic sets"],"prefix":"10.1007","volume":"199","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1043-393X","authenticated-orcid":false,"given":"Lea","family":"Kapelevich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1305-0141","authenticated-orcid":false,"given":"Chris","family":"Coey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4335-7248","authenticated-orcid":false,"given":"Juan Pablo","family":"Vielma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,10]]},"reference":[{"issue":"1","key":"1831_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","volume":"95","author":"F Alizadeh","year":"2003","unstructured":"Alizadeh, F., Goldfarb, D.: Second-order cone programming. 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