{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:07:47Z","timestamp":1760954867718},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2006,6,7]],"date-time":"2006-06-07T00:00:00Z","timestamp":1149638400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2007,3,27]]},"DOI":"10.1007\/s10107-006-0004-5","type":"journal-article","created":{"date-parts":[[2006,6,6]],"date-time":"2006-06-06T13:18:45Z","timestamp":1149599925000},"page":"315-336","source":"Crossref","is-referenced-by-count":23,"title":["An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems Over Symmetric Cones"],"prefix":"10.1007","volume":"110","author":[{"given":"Masakazu","family":"Kojima","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masakazu","family":"Muramatsu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2006,6,7]]},"reference":[{"key":"4_CR1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","volume":"95","author":"F. Alizadeh","year":"2003","unstructured":"Alizadeh F., Goldfarb D. (2003) Second-order cone programming. Math. Program. 95: 3\u201351","journal-title":"Math. Program."},{"key":"4_CR2","doi-asserted-by":"crossref","first-page":"2825","DOI":"10.1090\/S0002-9947-00-02472-7","volume":"352","author":"R.E. Curto","year":"2000","unstructured":"Curto R.E., Fialkow L.A. (2000) The truncated complex K-moment problem. Trans. Am. Math. Soc. 352: 2825\u20132855","journal-title":"Trans. Am. Math. Soc."},{"key":"4_CR3","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1023\/A:1009701824047","volume":"1","author":"L. Faybusovich","year":"1997","unstructured":"Faybusovich L. (1997) Euclidean Jordan algebras and interior-point algorithms. J. Positivity 1: 331\u2013357","journal-title":"J. Positivity"},{"key":"4_CR4","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0377-0427(97)00153-2","volume":"86","author":"L. Faybusovich","year":"1997","unstructured":"Faybusovich L.(1997) Linear systems in jordan algebras and primal-dual interior-point algorithms. J. Comput. Appl. Math. 86: 149\u2013175","journal-title":"J. Comput. Appl. Math."},{"key":"4_CR5","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534778.001.0001","volume-title":"Analysis on symmetric cones","author":"J. Faraut","year":"1994","unstructured":"Faraut J., Kor\u00e1nyi A. (1994) Analysis on symmetric cones. Oxford University Press, New York"},{"issue":"2","key":"4_CR6","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1145\/779359.779363","volume":"29","author":"D. Henrion","year":"2003","unstructured":"Henrion D., Lasserre J.B. (2003) GloptiPoly: global optimization over polynomials with Matlab and SeDuMi. ACM Trans. Math. Software 29(2): 165\u2013194","journal-title":"ACM Trans. Math. Software"},{"issue":"2","key":"4_CR7","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/TAC.2005.863494","volume":"51","author":"D. Henrion","year":"2006","unstructured":"Henrion D., Lasserre J.B. (2006) Convergent relaxations of polynomial matrix inequalities and static output feedback. IEEE Trans. Automat. Cont. 51(2): 192\u2013202","journal-title":"IEEE Trans. Automat. Cont."},{"key":"4_CR8","unstructured":"Hol C.W.J., Scherer C.W. Sum of squares relaxations for polynomial semi-definite programming. In: De Moor B., Motmans B. (eds.) Proceedings of the 16th International Symposium on Mahematical Theory of Networks and Systems. Leuven, Belgium, 5\u20139 July, 2004, pp. 1\u201310"},{"issue":"3","key":"4_CR9","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1137\/030601260","volume":"15","author":"S. Kim","year":"2005","unstructured":"Kim S., Kojima M., Waki H. (2005) Generalized Lagrangian duals and sums of squares relaxation of sparse polynomial optimization problems. SIAM J. Optim. 15(3): 697\u2013719","journal-title":"SIAM J. Optim."},{"key":"4_CR10","unstructured":"Kojima M. Sums of squares relaxations of polynomial semidefinite programs. Research Report B-397, Dept. of Mathematical and computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, November 2003"},{"issue":"2","key":"4_CR11","first-page":"125","volume":"46","author":"M. Kojima","year":"2003","unstructured":"Kojima M., Kim S., Waki H. (2003) A general framework for convex relaxation of polynomial optimization problems over cones. J. Oper. Res. Soc. Japan 46(2): 125\u2013144","journal-title":"J. Oper. Res. Soc. Japan"},{"issue":"1","key":"4_CR12","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10107-004-0554-3","volume":"103","author":"M. Kojima","year":"2004","unstructured":"Kojima M., Kim S., Waki H. (2004) Sparsity in sums of squares of polynomials. Math. Program. 103(1): 45\u201362","journal-title":"Math. Program."},{"key":"4_CR13","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"J.B. Lasserre","year":"2001","unstructured":"Lasserre J.B. (2001) Global optimization with polynomials and the problems of moments. SIAM J. Optim. 11: 796\u2013817","journal-title":"SIAM J. Optim."},{"issue":"3","key":"4_CR14","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1023\/A:1017920200889","volume":"112","author":"M. Muramatsu","year":"2002","unstructured":"Muramatsu M. (2002) On a commutative class of search directions for linear programming over symmetric cones. J. Optim. Theory Appl. 112(3): 595\u2013625","journal-title":"J. Optim. Theory Appl."},{"key":"4_CR15","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1137\/S1052623495290209","volume":"8","author":"Y.E. Nesterov","year":"1998","unstructured":"Nesterov Y.E., Todd M.J. (1998) Primal-dual interior-point methods for self-scaled cones. SIAM J. Optim. 8: 324\u2013364","journal-title":"SIAM J. Optim."},{"key":"4_CR16","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s10107-003-0387-5","volume":"96","author":"P.A. Parrilo","year":"2003","unstructured":"Parrilo P.A. (2003) Semidefinite programming relaxations for semialgebraic problems. Math. Program. 96: 293\u2013320","journal-title":"Math. Program."},{"key":"4_CR17","unstructured":"Prajna S., Papachristodoulou A., Parrilo P.A.: SOSTOOLS: sum of squares optimization toolbox for MATLAB \u2013 user\u2019s guide. Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125 USA, 2002"},{"key":"4_CR18","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1512\/iumj.1993.42.42045","volume":"42","author":"M. Putinar","year":"1993","unstructured":"Putinar M. (1993) Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42: 969\u2013984","journal-title":"Indiana Univ. Math. J."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-006-0004-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-006-0004-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-006-0004-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T17:51:11Z","timestamp":1707069071000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-006-0004-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6,7]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,3,27]]}},"alternative-id":["4"],"URL":"https:\/\/doi.org\/10.1007\/s10107-006-0004-5","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6,7]]}}}