{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T05:34:37Z","timestamp":1791092077893,"version":"4.1.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T00:00:00Z","timestamp":1131926400000},"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":[[2006,5]]},"DOI":"10.1007\/s10107-005-0672-6","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T10:26:37Z","timestamp":1131963997000},"page":"587-606","source":"Crossref","is-referenced-by-count":121,"title":["Minimizing Polynomials via Sum of Squares over the Gradient Ideal"],"prefix":"10.1007","volume":"106","author":[{"given":"Jiawang","family":"Nie","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Demmel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernd","family":"Sturmfels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2005,11,14]]},"reference":[{"key":"672_CR1","doi-asserted-by":"crossref","unstructured":"Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer-Verlag, 2003","DOI":"10.1007\/978-3-662-05355-3"},{"key":"672_CR2","doi-asserted-by":"crossref","unstructured":"Berg, C.: The multidimensional moment problem and semi-groups. In: Moments in Mathematics, H.J. Landau (ed.), AMS, Providence, RI, 1980, pp 110\u2013124","DOI":"10.1090\/psapm\/037\/921086"},{"key":"672_CR3","doi-asserted-by":"crossref","unstructured":"Bochnak, J., Coste, M., Roy, M-F.: Real Algebraic Geometry, Springer, 1998","DOI":"10.1007\/978-3-662-03718-8"},{"key":"672_CR4","unstructured":"Blekherman, G.: There are significantly more nonnegative polynomials than sums of squares. To appear in Israel Journal of Mathematics"},{"key":"672_CR5","doi-asserted-by":"crossref","unstructured":"Becker, E., Neuhaus, R.: Computation of real radicals of polynomial ideals. Computational algebraic geometry (Nice, 1992), 1\u201320, Progress in Mathematics, 109, Birkh\u00e4user, Boston, MA, 1993","DOI":"10.1007\/978-1-4612-2752-6_1"},{"key":"672_CR6","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/S0022-4049(96)00103-X","volume":"124","author":"Becker","year":"1998","unstructured":"Becker, E., Neuhaus, R.: Computation of real radicals of polynomial ideals. II. J. Pure Appl. Algebra 124, 261\u2013280 (1998)","journal-title":"II. J. Pure Appl. Algebra"},{"key":"672_CR7","unstructured":"Cox, D.A., Little, J.B., D.O'Shea.: Ideals, Varieties and Algorithms: an Introduction to Computational Algebraic Geometry and Commutative Algebra, Second Edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1997"},{"key":"672_CR8","doi-asserted-by":"crossref","unstructured":"Cox, D.A., Little, J.B., D.O'Shea.: Using Algebraic Geometry, Graduate Texts in Mathematics, Vol. 185. Springer-Verlag, New York, 1998","DOI":"10.1007\/978-1-4757-6911-1"},{"key":"672_CR9","doi-asserted-by":"crossref","unstructured":"Corless, R.M., Gianni, P.M., Trager, B.M.: A reorder Schur factorization method for zero-dimensional polynomial systems with multiple roots. Proc. ACM Int. Symp. Symbolic and Algebraic Computation, Maui, Hawaii, 1997, pp 133\u2013140","DOI":"10.1145\/258726.258767"},{"key":"672_CR10","doi-asserted-by":"crossref","first-page":"2825","DOI":"10.1090\/S0002-9947-00-02472-7","volume":"352","author":"Curto","year":"2000","unstructured":"Curto, R.E., Fialkow, L.A.: The truncated complex K-moment problem. Trans. Am. Math. Soc. 352, 2825\u20132855 (2000)","journal-title":"Trans. Am. Math. Soc."},{"key":"672_CR11","doi-asserted-by":"crossref","unstructured":"Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, Vol. 150. Springer-Verlag, New York, 1995","DOI":"10.1007\/978-1-4612-5350-1"},{"key":"672_CR12","doi-asserted-by":"crossref","unstructured":"Fortuna, E., Gianni, P., Trager, B.: Derivations and radicals of polynomial ideals over fields of arbitrary characteristic. Computer algebra (London, ON, 2001). J. Symbolic Comput. 33 (5), 609\u2013625 (2002)","DOI":"10.1006\/jsco.2002.0525"},{"key":"672_CR13","doi-asserted-by":"crossref","unstructured":"Grigoriev, D., Vorobjov, N. N., Jr. Solving systems of polynomial inequalities in subexponential time. J. Symbolic Comput. 5 (1\u20132), 37\u201364 (1988)","DOI":"10.1016\/S0747-7171(88)80005-1"},{"key":"672_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1024664432540","volume":"27","author":"Hanzon","year":"2003","unstructured":"Hanzon, B., Jibetean, D.: Global minimization of a multivariate polynomial using matrix methods. J. Global Optimization 27, 1\u201323 (2003)","journal-title":"J. Global Optimization"},{"key":"672_CR15","doi-asserted-by":"crossref","unstructured":"Henrion, D., Lasserre, J. B.: GloptiPoly: Global Optimization over Polynomials with Matlab and SeDuMi. Proceeding of the 41st IEEE Conference on Decision and Control (CDC'2002), Las Vegas, Nevada, December 10\u201313, 2002, pp 747\u2013752","DOI":"10.1145\/779359.779363"},{"key":"672_CR16","doi-asserted-by":"crossref","unstructured":"Henrion, D., Lasserre, J.: Detecting global optimality and extracting solutions in GloptiPoly. Positive polynomials in control, D. Henrion, A. Garulli Eds., Lecture Notes on Control and Information Sciences, Vol. 312, Springer, Berlin, 2005, pp 293\u2013310","DOI":"10.1007\/10997703_15"},{"key":"672_CR17","unstructured":"Jibetean, D., Laurent, M.: Converging SDP bounds for global unconstrained polynomial optimization. Preprint, 2004. Website: http:\/\/www.cwi.nl\/~monique"},{"key":"672_CR18","doi-asserted-by":"crossref","unstructured":"Krick, T., Logar, A.: An algorithm for the computation of the radical of an ideal in the ring of polynomials. Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991), Lecture Notes in Comput. Sci., 539, Springer, Berlin, 1991, pp 195\u2013205","DOI":"10.1007\/3-540-54522-0_108"},{"key":"672_CR19","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"Lasserre","year":"3","unstructured":"Lasserre, J.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11 (3), 796\u2013817 (2001)","journal-title":"SIAM J. Optim."},{"key":"672_CR20","unstructured":"Laurent, M.: Semidefinite representations for finite varieties. To appear in Mathematical Programming. Website: http:\/\/www.cwi.nl\/~monique"},{"key":"672_CR21","doi-asserted-by":"crossref","first-page":"575","DOI":"10.4153\/CMB-2003-054-7","volume":"46","author":"Marshall","year":"2003","unstructured":"Marshall, M.: Optimization of polynomial functions. Canad. Math. Bull. 46, 575\u2013587 (2003)","journal-title":"Canad. Math. Bull."},{"key":"672_CR22","doi-asserted-by":"crossref","unstructured":"Nesterov, Y.: Squared functional systems and optimization problems. High Performance Optimization H. Frenk et al. (eds.), Kluwer Academic Publishers, 2000, pp 405\u2013440","DOI":"10.1007\/978-1-4757-3216-0_17"},{"key":"672_CR23","unstructured":"Nie, J., Demmel, J. W.: Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares, to appear in J. Global Optimization, arXiv:math.OC\/0411122"},{"key":"672_CR24","unstructured":"Nie, J., Demmel, J. W., Powers, V.: Representations of positive polynomials on non-compact semialgebraic sets via KKT ideals. Preprint, 2005"},{"key":"672_CR25","doi-asserted-by":"crossref","unstructured":"Nocedal, J., Wright, S. J.: Numerical Optimization, Springer Series in Operations Research, Springer-Verlag, New York, 1999","DOI":"10.1007\/b98874"},{"key":"672_CR26","unstructured":"Parrilo, P.: Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization, Ph.D Thesis, California Institute of Technology, 2000"},{"key":"672_CR27","doi-asserted-by":"crossref","unstructured":"Parrilo, P., Sturmfels, B.: Minimizing polynomial functions, Proceedings of the DIMACS Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science (March 2001), S. Basu, L. Gonzalez-Vega (eds.), American Mathematical Society, 2003, pp 83\u2013100","DOI":"10.1090\/dimacs\/060\/08"},{"key":"672_CR28","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s10107-003-0387-5","volume":"96","author":"Parrilo","year":"2","unstructured":"Parrilo, P.: Semidefinite Programming relaxations for semialgebraic problems. Math. Program. Ser. B 96 (2), 293\u2013320 (2003)","journal-title":"Math. Program. Ser. B"},{"key":"672_CR29","unstructured":"Prajna, S., Papachristodoulou, A., Parrilo, P.: SOSTOOLS User's Guide. http:\/\/control.ee.ethz.ch\/~parrilo\/SOSTOOLS\/"},{"key":"672_CR30","unstructured":"Parrilo, P.: An explicit construction of distinguished representations of polynomials nonnegative over finite sets, If A Technical Report AUT02-02, March 2002"},{"key":"672_CR31","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1512\/iumj.1993.42.42045","volume":"42","author":"Putinar","year":"1993","unstructured":"Putinar, M.: Positive polynomials on compact semi-algebraic sets. Ind. Univ. Math. J. 42, 203\u2013206 (1993)","journal-title":"Ind. Univ. Math. J."},{"key":"672_CR32","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0747-7171(10)80003-3","volume":"13","author":"Renegar","year":"3","unstructured":"Renegar, J.: On the computational complexity and geometry of the first-order theory of the reals. I-III. J. Symbolic Comput. 13 (3), 255\u2013352 (1992)","journal-title":"I-III. J. Symbolic Comput."},{"key":"672_CR33","doi-asserted-by":"crossref","unstructured":"Reznick, B.: Some concrete aspects of Hilbert's 17 th problem. In Contemporary Mathematics, volume 253, American Mathematical Society, 2000, pp 251\u2013272","DOI":"10.1090\/conm\/253\/03936"},{"key":"672_CR34","doi-asserted-by":"crossref","unstructured":"Shafarevich. Basic algebraic geometry. Die Grundlehren der mathematischen Wissenschaften. Band 213. Springer-Verlag, 1974","DOI":"10.1007\/978-3-642-96200-4"},{"key":"672_CR35","doi-asserted-by":"crossref","unstructured":"L. Vandenberghe and S. Boyd. Semidefinite Programming. SIAM Review 38, 49\u201395 (1996)","DOI":"10.1137\/1038003"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-005-0672-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-005-0672-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-005-0672-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T17:23:11Z","timestamp":1586539391000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-005-0672-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,14]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,5]]}},"alternative-id":["672"],"URL":"https:\/\/doi.org\/10.1007\/s10107-005-0672-6","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,11,14]]}}}