{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T09:28:46Z","timestamp":1763544526367,"version":"build-2065373602"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2011,6,5]],"date-time":"2011-06-05T00:00:00Z","timestamp":1307232000000},"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":[[2011,10]]},"DOI":"10.1007\/s10107-011-0464-0","type":"journal-article","created":{"date-parts":[[2011,6,4]],"date-time":"2011-06-04T04:46:29Z","timestamp":1307162789000},"page":"357-382","source":"Crossref","is-referenced-by-count":40,"title":["Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems"],"prefix":"10.1007","volume":"129","author":[{"given":"Anthony Man-Cho","family":"So","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,6,5]]},"reference":[{"issue":"2","key":"464_CR1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s10208-005-0178-x","volume":"7","author":"A. Barvinok","year":"2007","unstructured":"Barvinok A.: Integration and optimization of multivariate polynomials by restriction onto a random subspace. Found. Comput. Math. 7(2), 229\u2013244 (2007)","journal-title":"Found. Comput. Math."},{"key":"464_CR2","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1112\/S0025579300014364","volume":"48","author":"A. Brieden","year":"2001","unstructured":"Brieden A., Gritzmann P., Kannan R., Klee V., Lov\u00e1sz L., Simonovits M.: Deterministic and randomized polynomial-time approximation of radii. Mathematika 48, 63\u2013105 (2001)","journal-title":"Mathematika"},{"key":"464_CR3","volume-title":"Matrix Computations","author":"G.H. Golub","year":"1996","unstructured":"Golub G.H., Van Loan C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"issue":"1","key":"464_CR4","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/BF02187841","volume":"7","author":"P. Gritzmann","year":"1992","unstructured":"Gritzmann P., Klee V.: Inner and outer j-radii of convex bodies in finite-dimensional normed spaces. Discret. Comput. Geom. 7(1), 255\u2013280 (1992)","journal-title":"Discret. Comput. Geom."},{"key":"464_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-78240-4","volume-title":"Geometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics, vol. 2, 2nd corrected edn","author":"M. Gr\u00f6tschel","year":"1993","unstructured":"Gr\u00f6tschel M., Lov\u00e1sz L., Schrijver A.: Geometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics, vol. 2, 2nd corrected edn. Springer, Berlin (1993)"},{"issue":"1","key":"464_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10659-009-9205-5","volume":"97","author":"D. Han","year":"2009","unstructured":"Han D., Dai H.H., Qi L.: Conditions for strong ellipticity of anisotropic elastic materials. J. Elast. 97(1), 1\u201313 (2009)","journal-title":"J. Elast."},{"key":"464_CR7","unstructured":"He, S., Li, Z., Zhang, S.: General constrained polynomial optimization: an approximation approach. Technical Report of SEEM2009\u201306, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong (2009)"},{"issue":"2","key":"464_CR8","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s10107-010-0409-z","volume":"125","author":"S. He","year":"2010","unstructured":"He S., Li Z., Zhang S.: Approximation algorithms for homogeneous polynomial optimization with quadratic constraints. Math. Program. Ser. B 125(2), 353\u2013383 (2010)","journal-title":"Math. Program. Ser. B"},{"key":"464_CR9","unstructured":"Hillar, C.J., Lim, L.H.: Most Tensor Problems are NP Hard (2009, Preprint)"},{"key":"464_CR10","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/978-3-642-12598-0_13","volume-title":"Recent Advances in Optimization and its Applications in Engineering","author":"M. Ishteva","year":"2010","unstructured":"Ishteva M., Absil P.A., van Huffel S., de Lathauwer L.: On the best low multilinear rank approximation of higher-order tensors. In: Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds) Recent Advances in Optimization and its Applications in Engineering, pp. 145\u2013164. Springer, Berlin (2010)"},{"key":"464_CR11","doi-asserted-by":"crossref","unstructured":"Kannan, R.: Spectral methods for matrices and tensors. In: Proceedings of the 42nd Annual ACM Symposium on Theory of Computing (STOC 2010), pp. 1\u201312 (2010)","DOI":"10.1145\/1806689.1806691"},{"issue":"4","key":"464_CR12","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1137\/070691140","volume":"38","author":"S. Khot","year":"2008","unstructured":"Khot S., Naor A.: Linear equations modulo 2 and the L 1 diameter of convex bodies. SIAM J. Comput. 38(4), 1448\u20131463 (2008)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"464_CR13","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10100-007-0052-9","volume":"16","author":"E. Klerk de","year":"2008","unstructured":"de Klerk E.: The complexity of optimizing over a simplex, hypercube or sphere: a short survey. Cent. Eur. J. Oper. Res. 16(2), 111\u2013125 (2008)","journal-title":"Cent. Eur. J. Oper. Res."},{"issue":"2\u20133","key":"464_CR14","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.tcs.2006.05.011","volume":"361","author":"E. Klerk de","year":"2006","unstructured":"de Klerk E., Laurent M., Parrilo P.A.: A PTAS for the minimization of polynomials of fixed degree over the simplex. Theor. Comput. Sci. 361(2\u20133), 210\u2013225 (2006)","journal-title":"Theor. Comput. Sci."},{"key":"464_CR15","doi-asserted-by":"crossref","unstructured":"Kofidis, E., Regalia, P.A.: Tensor approximation and signal processing applications. In: Olshevsky, V. (ed.) Structured Matrices in Mathematics, Computer Science and Engineering I: Proceedings of an AMS\u2013IMS\u2013SIAM Joint Summer Research Conference, Contemporary Mathematics, vol. 280, pp. 103\u2013133. American Mathematical Society, Providence, Rhode Island (2001)","DOI":"10.1090\/conm\/280\/04625"},{"issue":"3","key":"464_CR16","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"T.G. Kolda","year":"2009","unstructured":"Kolda T.G., Bader B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"issue":"3","key":"464_CR17","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1214\/aop\/1176992081","volume":"15","author":"S. Kwapien","year":"1987","unstructured":"Kwapien S.: Decoupling inequalities for polynomial chaos. Ann. Probab. 15(3), 1062\u20131071 (1987)","journal-title":"Ann. Probab."},{"issue":"3","key":"464_CR18","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"J.B. Lasserre","year":"2001","unstructured":"Lasserre J.B.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796\u2013817 (2001)","journal-title":"SIAM J. Optim."},{"key":"464_CR19","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/978-0-387-09686-5_7","volume-title":"Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and Its Applications, vol. 149","author":"M. Laurent","year":"2009","unstructured":"Laurent M.: Sums of squares, moment matrices and optimization over polynomials. In: Putinar, M., Sullivant, S. (eds) Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and Its Applications, vol. 149, pp. 157\u2013270. Springer Science+Business Media, LLC, New York (2009)"},{"issue":"6","key":"464_CR20","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.crme.2010.06.005","volume":"338","author":"L.H. Lim","year":"2010","unstructured":"Lim L.H., Comon P.: Multiarray signal processing: tensor decomposition meets compressed sensing. Comptes Rendus M\u00e9canique 338(6), 311\u2013320 (2010)","journal-title":"Comptes Rendus M\u00e9canique"},{"issue":"3","key":"464_CR21","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1137\/080729104","volume":"20","author":"C. Ling","year":"2009","unstructured":"Ling C., Nie J., Qi L., Ye Y.: Biquadratic optimization over unit spheres and semidefinite programming relaxations. SIAM J. Optim. 20(3), 1286\u20131310 (2009)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"464_CR22","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1137\/090772952","volume":"20","author":"Z.Q. Luo","year":"2010","unstructured":"Luo Z.Q., Zhang S.: A semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraints. SIAM J. Optim. 20(4), 1716\u20131736 (2010)","journal-title":"SIAM J. Optim."},{"key":"464_CR23","unstructured":"Nesterov, Yu.: Random walk in a simplex and quadratic optimization over convex polytopes. CORE Discussion Paper 2003071, Universit\u00e9 Catholique de Louvain, Belgium (2003)"},{"key":"464_CR24","unstructured":"Nie, J.: An approximation bound analysis for Lasserre\u2019s relaxation in multivariate polynomial optimization (2009, Preprint)"},{"key":"464_CR25","unstructured":"Parrilo, P.A.: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D. thesis, California Institute of Technology, Pasadena (2000)"},{"issue":"6","key":"464_CR26","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1016\/j.jsc.2005.05.007","volume":"40","author":"L. Qi","year":"2005","unstructured":"Qi L.: Eigenvalues of a real supersymmetric tensor. J. Symbol. Comput. 40(6), 1302\u20131324 (2005)","journal-title":"J. Symbol. Comput."},{"issue":"2","key":"464_CR27","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s11464-009-0016-6","volume":"4","author":"L. Qi","year":"2009","unstructured":"Qi L., Dai H.H., Han D.: Conditions for strong ellipticity and M-Eigenvalues. Front. Math. China 4(2), 349\u2013364 (2009)","journal-title":"Front. Math. China"},{"issue":"2","key":"464_CR28","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s10107-007-0193-6","volume":"118","author":"L. Qi","year":"2009","unstructured":"Qi L., Wang F., Wang Y.: Z-Eigenvalue methods for a global polynomial optimization problem. Math. Program. Ser. A 118(2), 301\u2013316 (2009)","journal-title":"Math. Program. Ser. A"},{"key":"464_CR29","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1090\/conm\/253\/03936","volume-title":"Real Algebraic Geometry and Ordered Structures, Contemporary Mathematics, vol. 253","author":"B. Reznick","year":"2000","unstructured":"Reznick B.: Some concrete aspects of Hilbert\u2019s 17th problem. In: Delzell, C.N., Madden, J.J. (eds) Real Algebraic Geometry and Ordered Structures, Contemporary Mathematics, vol. 253, pp. 251\u2013272. American Mathematical Society, Providence Rhode Island (2000)"},{"issue":"4","key":"464_CR30","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1287\/moor.1080.0326","volume":"33","author":"A.M.C. So","year":"2008","unstructured":"So A.M.C., Ye Y., Zhang J.: A unified theorem on SDP rank reduction. Math. Oper. Res. 33(4), 910\u2013920 (2008)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"464_CR31","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1109\/TSP.2009.2034308","volume":"58","author":"S. Weiland","year":"2010","unstructured":"Weiland S., van Belzen F.: Singular value decompositions and low rank approximations of tensors. IEEE Trans. Signal Process. 58(3), 1171\u20131182 (2010)","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-011-0464-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-011-0464-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-011-0464-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T12:02:35Z","timestamp":1560254555000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-011-0464-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,5]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["464"],"URL":"https:\/\/doi.org\/10.1007\/s10107-011-0464-0","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2011,6,5]]}}}