{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T15:45:22Z","timestamp":1726847122261},"reference-count":26,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2007,2,1]],"date-time":"2007-02-01T00:00:00Z","timestamp":1170288000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":2358,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Complexity"],"published-print":{"date-parts":[[2007,2]]},"DOI":"10.1016\/j.jco.2006.07.002","type":"journal-article","created":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T07:38:46Z","timestamp":1160552326000},"page":"135-150","source":"Crossref","is-referenced-by-count":96,"title":["On the complexity of Putinar's Positivstellensatz"],"prefix":"10.1016","volume":"23","author":[{"given":"Jiawang","family":"Nie","sequence":"first","affiliation":[]},{"given":"Markus","family":"Schweighofer","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jco.2006.07.002_bib1","article-title":"Real algebraic geometry","volume":"vol. 36","author":"Bochnak","year":"1998"},{"key":"10.1016\/j.jco.2006.07.002_bib2","unstructured":"J. Demmel, J. Nie, V. Powers, Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals, J. Pure Appl. Algebra, to appear \u3008http:\/\/math.berkeley.edu\/\u223cnjw\/\u3009."},{"key":"10.1016\/j.jco.2006.07.002_bib3","unstructured":"D. Henrion, J. Lasserre, GloptiPoly: global optimization over polynomials with Matlab and SeDuMi \u3008http:\/\/www.laas.fr\/\u223chenrion\/software\/gloptipoly\/\u3009."},{"key":"10.1016\/j.jco.2006.07.002_bib4","first-page":"223","article-title":"Distinguished representations of strictly positive polynomials","volume":"532","author":"Jacobi","year":"2001","journal-title":"J. Reine Angew. Math."},{"issue":"2","key":"10.1016\/j.jco.2006.07.002_bib5","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1137\/04060562X","article-title":"Semidefinite approximations for global unconstrained polynomial optimization","volume":"16","author":"Jibetean","year":"2005","journal-title":"SIAM J. Optim."},{"issue":"1A","key":"10.1016\/j.jco.2006.07.002_bib6","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10107-004-0554-3","article-title":"Sparsity in sums of squares of polynomials","volume":"103","author":"Kojima","year":"2005","journal-title":"Math. Program."},{"issue":"3","key":"10.1016\/j.jco.2006.07.002_bib7","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","article-title":"Global optimization with polynomials and the problem of moments","volume":"11","author":"Lasserre","year":"2001","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.jco.2006.07.002_bib8","unstructured":"J. L\u00f6fberg, YALMIP: A MATLAB toolbox for rapid prototyping of optimization problems \u3008http:\/\/control.ee.ethz.ch\/\u223cjoloef\/yalmip.php\u3009."},{"issue":"4","key":"10.1016\/j.jco.2006.07.002_bib9","doi-asserted-by":"crossref","first-page":"575","DOI":"10.4153\/CMB-2003-054-7","article-title":"Optimization of polynomial functions","volume":"46","author":"Marshall","year":"2003","journal-title":"Can. Math. Bull."},{"key":"10.1016\/j.jco.2006.07.002_bib10","doi-asserted-by":"crossref","unstructured":"M. Marshall, Representation of non-negative polynomials with finitely many zeros, Ann. Facult\u00e9 Sci. Toulouse, S\u00e9r. 6, 15 (3) (2006) 599\u2013609.","DOI":"10.5802\/afst.1131"},{"issue":"3A","key":"10.1016\/j.jco.2006.07.002_bib11","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s10107-005-0672-6","article-title":"Minimizing polynomials via sum of squares over the gradient ideal","volume":"106","author":"Nie","year":"2006","journal-title":"Math. Program."},{"key":"10.1016\/j.jco.2006.07.002_bib12","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1090\/dimacs\/060\/08","article-title":"Minimizing polynomial functions","volume":"60","author":"Parrilo","year":"2003","journal-title":"DIMACS Ser. Discrete Math. Theoret. Comput. Sci."},{"key":"10.1016\/j.jco.2006.07.002_bib13","first-page":"141","article-title":"\u00dcber positive Darstellung von Polynomen","volume":"73","author":"P\u00f3lya","year":"1928","journal-title":"Vierteljahresschrift der Naturforschenden Gesellschaft in Z\u00fcrich"},{"issue":"1\u20132","key":"10.1016\/j.jco.2006.07.002_bib14","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0022-4049(00)00155-9","article-title":"A new bound for P\u00f3lya's theorem with applications to polynomials positive on polyhedra","volume":"164","author":"Powers","year":"2001","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/j.jco.2006.07.002_bib15","unstructured":"S. Prajna, A. Papachristodoulou, P. Seiler, P. Parrilo, SOSTOOLS: Sum of Squares Optimization Toolbox for MATLAB \u3008http:\/\/www.cds.caltech.edu\/sostools\/\u3009."},{"key":"10.1016\/j.jco.2006.07.002_bib16","first-page":"253","article-title":"Bounds for representations of polynomials positive on compact semi-algebraic sets","volume":"32","author":"Prestel","year":"2002","journal-title":"Fields Inst. Commun."},{"key":"10.1016\/j.jco.2006.07.002_bib17","series-title":"Positive Polynomials, Springer Monographs in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-04648-7","author":"Prestel","year":"2001"},{"issue":"3","key":"10.1016\/j.jco.2006.07.002_bib18","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1512\/iumj.1993.42.42045","article-title":"Positive polynomials on compact semi-algebraic sets","volume":"42","author":"Putinar","year":"1993","journal-title":"Indiana Univ. Math. J."},{"issue":"2","key":"10.1016\/j.jco.2006.07.002_bib19","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.jalgebra.2005.01.043","article-title":"Distinguished representations of non-negative polynomials","volume":"289","author":"Scheiderer","year":"2005","journal-title":"J. Algebra"},{"issue":"2","key":"10.1016\/j.jco.2006.07.002_bib20","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01446568","article-title":"The K-moment problem for compact semi-algebraic sets","volume":"289","author":"Schm\u00fcdgen","year":"1991","journal-title":"Math. Ann."},{"issue":"3","key":"10.1016\/j.jco.2006.07.002_bib21","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/S0022-4049(01)00041-X","article-title":"An algorithmic approach to Schm\u00fcdgen's Positivstellensatz","volume":"166","author":"Schweighofer","year":"2002","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/j.jco.2006.07.002_bib22","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/j.jco.2004.01.005","article-title":"On the complexity of Schm\u00fcdgen's Positivstellensatz","volume":"20","author":"Schweighofer","year":"2004","journal-title":"J. Complexity"},{"issue":"3","key":"10.1016\/j.jco.2006.07.002_bib23","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1137\/S1052623403431779","article-title":"Optimization of polynomials on compact semialgebraic sets","volume":"15","author":"Schweighofer","year":"2005","journal-title":"SIAM J. Optim."},{"issue":"4","key":"10.1016\/j.jco.2006.07.002_bib24","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s00229-005-0568-z","article-title":"Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets","volume":"117","author":"Schweighofer","year":"2005","journal-title":"Manuscripta Math."},{"issue":"2","key":"10.1016\/j.jco.2006.07.002_bib25","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1006\/jcom.1996.0011","article-title":"Complexity estimates for the Schm\u00fcdgen Positivstellensatz","volume":"12","author":"Stengle","year":"1996","journal-title":"J. Complexity"},{"key":"10.1016\/j.jco.2006.07.002_bib26","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1017\/S0962492901000071","article-title":"Semidefinite optimization","volume":"10","author":"Todd","year":"2001","journal-title":"Acta Numer."}],"container-title":["Journal of Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X0600080X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X0600080X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,21]],"date-time":"2019-04-21T12:27:03Z","timestamp":1555849623000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0885064X0600080X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,2]]}},"alternative-id":["S0885064X0600080X"],"URL":"https:\/\/doi.org\/10.1016\/j.jco.2006.07.002","relation":{},"ISSN":["0885-064X"],"issn-type":[{"value":"0885-064X","type":"print"}],"subject":[],"published":{"date-parts":[[2007,2]]}}}