{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T03:58:24Z","timestamp":1727063904384},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2016,11,15]],"date-time":"2016-11-15T00:00:00Z","timestamp":1479168000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s11590-016-1094-5","type":"journal-article","created":{"date-parts":[[2016,11,15]],"date-time":"2016-11-15T04:27:38Z","timestamp":1479184058000},"page":"1767-1782","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Improved approximation results on standard quartic polynomial optimization"],"prefix":"10.1007","volume":"11","author":[{"given":"Chen","family":"Ling","sequence":"first","affiliation":[]},{"given":"Hongjin","family":"He","sequence":"additional","affiliation":[]},{"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,15]]},"reference":[{"key":"1094_CR1","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1023\/A:1020209017701","volume":"24","author":"IM Bomze","year":"2002","unstructured":"Bomze, I.M., De Klerk, E.: Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. J. Glob. Optim. 24, 163\u2013185 (2002)","journal-title":"J. Glob. Optim."},{"key":"1094_CR2","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s10898-013-0126-2","volume":"59","author":"IM Bomze","year":"2014","unstructured":"Bomze, I.M., Gollowitzer, S., Y\u0131ld\u0131r\u0131m, E.A.: Rounding on the standard simplex: Regular grids for global optimization. J. Glob. Optim. 59, 243\u2013258 (2014)","journal-title":"J. Glob. Optim."},{"key":"1094_CR3","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0021-9045(83)90140-5","volume":"38","author":"LP Bos","year":"1983","unstructured":"Bos, L.P.: Bounding the Lebesgue function for Lagrange interpolation in a simplex. J. Approx. Theory 38, 43\u201359 (1983)","journal-title":"J. Approx. Theory"},{"key":"1094_CR4","doi-asserted-by":"crossref","unstructured":"Burer, S.: Copositive Programming, chap.\u00a08, pp. 201\u2013218. Handbook on Semidefinite, Conic and Polynomial Optimization. Springer, Boston, MA (2012)","DOI":"10.1007\/978-1-4614-0769-0_8"},{"key":"1094_CR5","doi-asserted-by":"crossref","unstructured":"De\u00a0Klerk, E.: The complexity of optimizing over a simplex, hypercube or sphere: A short survey. Cent. Eur. J. Oper. Res. 16 (2008)","DOI":"10.1007\/s10100-007-0052-9"},{"key":"1094_CR6","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, 210\u2013225 (2006)","journal-title":"Theor. Comput. Sci."},{"key":"1094_CR7","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s10107-014-0825-6","volume":"151","author":"E Klerk De","year":"2014","unstructured":"De Klerk, E., Laurent, M., Sun, Z.: An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex. Math. Program. 151, 433\u2013457 (2014)","journal-title":"Math. Program."},{"key":"1094_CR8","volume-title":"Inequalities","author":"GH Hardy","year":"1952","unstructured":"Hardy, G.H., Littlewood, J.E., P\u00f3lya, G.: Inequalities, 2nd edn. Cambridge University Press, Cambridge (1952)","edition":"2"},{"key":"1094_CR9","volume-title":"Introduction to Global Optimization","author":"R Horst","year":"1995","unstructured":"Horst, R., Pardalos, P., Thoai, N.: Introduction to Global Optimization. Kluwer Academic Publishers, London (1995)"},{"key":"1094_CR10","unstructured":"Li, Z.: Polynomial optimization problems: Approximation algorithms and applications. Ph.D. thesis, The Chinese University of Hong Kong (2011)"},{"key":"1094_CR11","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1137\/090772952","volume":"20","author":"Z Luo","year":"2010","unstructured":"Luo, Z., Zhang, S.: A semidefinite relaxation scheme for multivariate quartic polynomial optimization with wuadratic constraints. SIAM J. Optim. 20, 1716\u20131736 (2010)","journal-title":"SIAM J. Optim."},{"key":"1094_CR12","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF02592948","volume":"39","author":"KG Murty","year":"1987","unstructured":"Murty, K.G., Kabadi, S.N.: Some NP-complete problems in quadratic and nonlinear programming. Math. Program. 39, 117\u2013129 (1987)","journal-title":"Math. Program."},{"key":"1094_CR13","unstructured":"P\u00f3lya, G.: \u00dcber positive darstelluny von polynomen vierteljschr. In: Naturforsch. Ges. Zurich, vol.\u00a073, pp. 141\u2013145. MIT Press, Zurich (1974)"},{"key":"1094_CR14","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0022-4049(00)00155-9","volume":"164","author":"V Powers","year":"2001","unstructured":"Powers, V., Reznick, B.: A new bound for P\u00f3lya\u2019s theorem with applications to polynomials positive on polyhedra. J. Pure Appl. Algebra 164, 221\u2013229 (2001)","journal-title":"J. Pure Appl. Algebra"},{"key":"1094_CR15","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.laa.2013.03.015","volume":"439","author":"L Qi","year":"2013","unstructured":"Qi, L.: Symmetric nonnegative tensors and copositive tensors. Linear Algebra Appl. 439, 228\u2013238 (2013)","journal-title":"Linear Algebra Appl."},{"key":"1094_CR16","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1137\/13092232X","volume":"35","author":"L Qi","year":"2014","unstructured":"Qi, L., Xu, C., Xu, Y.: Nonnegative tensor factorization, completely positive tensors, and a hierarchical elimination algorithm. SIAM J. Matrix Anal. Appl. 35, 1227\u20131241 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1094_CR17","series-title":"MPS\/SIAM Series on Optimization","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718812","volume-title":"A Mathematical View of Interior-Point Methods in Convex Optimization","author":"J Renegar","year":"2001","unstructured":"Renegar, J.: A Mathematical View of Interior-Point Methods in Convex Optimization. MPS\/SIAM Series on Optimization. SIAM, Philadelphia, PA (2001)"},{"key":"1094_CR18","volume-title":"Analysis of Copositive Optimization Based Bounds on Standard Quadratic Optimization","author":"G Sagol","year":"2013","unstructured":"Sagol, G., Y\u0131ld\u0131r\u0131m, E.A.: Analysis of Copositive Optimization Based Bounds on Standard Quadratic Optimization. Department of Industrial Engineering, Koc University, Sariyer, Istanbul (2013). Tech. rep."},{"key":"1094_CR19","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s10107-011-0464-0","volume":"129","author":"AMC So","year":"2011","unstructured":"So, A.M.C.: Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems. Math. Progr. 129, 357\u2013382 (2011)","journal-title":"Math. Progr."},{"key":"1094_CR20","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1080\/03081087.2013.851198","volume":"63","author":"Y Song","year":"2015","unstructured":"Song, Y., Qi, L.: Necessary and sufficient conditions for copositive tensors. Linear Multilinear A 63, 120\u2013131 (2015)","journal-title":"Linear Multilinear A"},{"key":"1094_CR21","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1080\/10556788.2010.540014","volume":"27","author":"EA Y\u0131ld\u0131r\u0131m","year":"2012","unstructured":"Y\u0131ld\u0131r\u0131m, E.A.: On the accuracy of uniform polyhedral approximations of the copositive cone. Optim. Method Softw. 27, 155\u2013173 (2012)","journal-title":"Optim. Method Softw."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-016-1094-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-016-1094-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-016-1094-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,15]],"date-time":"2019-09-15T15:48:05Z","timestamp":1568562485000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-016-1094-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,15]]},"references-count":21,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["1094"],"URL":"https:\/\/doi.org\/10.1007\/s11590-016-1094-5","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,15]]}}}