{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T07:26:31Z","timestamp":1746861991498},"reference-count":33,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,4,1]],"date-time":"2011-04-01T00:00:00Z","timestamp":1301616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>In this paper, we consider the NP\u2010hard problem of finding global minimum of quadratically constrained multivariate bi\u2010quadratic optimization. We present some bounds of the considered problem via approximately solving the related bi\u2010linear semidefinite programming (SDP) relaxation. Based on the bi\u2010linear SDP relaxation, we also establish some approximation solution methods, which generalize the methods for the quadratic polynomial optimization in (<jats:italic>SIAM J. Optim.<\/jats:italic> 2003; <jats:bold>14<\/jats:bold>:268\u2013283). Finally, we present a special form, whose bi\u2010linear SDP relaxation can be approximately solved in polynomial time. Copyright \u00a9 2011 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.781","type":"journal-article","created":{"date-parts":[[2011,4,1]],"date-time":"2011-04-01T05:17:34Z","timestamp":1301635054000},"page":"113-131","source":"Crossref","is-referenced-by-count":13,"title":["Semidefinite relaxation approximation for multivariate bi\u2010quadratic optimization with quadratic constraints"],"prefix":"10.1002","volume":"19","author":[{"given":"Chen","family":"Ling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinzhen","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,4]]},"reference":[{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401395899"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-010-0409-z"},{"key":"e_1_2_7_4_2","unstructured":"HeS LiZ ZhangS General constrained polynomial optimization: an approximation approach. Technical Report SEEM2009\u201006 Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong 2009."},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/080729104"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/090772952"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-010-9545-5"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1162\/089976699300016863"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(94)90029-9"},{"key":"e_1_2_7_10_2","unstructured":"De LathauwerL ComonP De MoorB VandewalleJ Higher\u2010order power method\u2014application in independent component analysis. Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA'95) Las Vegas NV 1995;91\u201396."},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898346995"},{"key":"e_1_2_7_12_2","volume-title":"Fast Reliable Algorithms for Structured Matrices","author":"Grigorascu VS","year":"1999"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00126996"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00279991"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801387413"},{"key":"e_1_2_7_16_2","volume-title":"A Nonlinear Signal Processing Framework","author":"Nikias CL","year":"1993"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-007-0193-6"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00377977"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251549"},{"key":"e_1_2_7_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00042193"},{"key":"e_1_2_7_21_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899352045"},{"key":"e_1_2_7_22_2","volume-title":"Frontiers in Global Optimization","author":"Faybusovich L","year":"2003"},{"key":"e_1_2_7_23_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009739827008"},{"key":"e_1_2_7_24_2","doi-asserted-by":"publisher","DOI":"10.1137\/070679041"},{"key":"e_1_2_7_25_2","doi-asserted-by":"publisher","DOI":"10.1137\/050642691"},{"key":"e_1_2_7_26_2","volume-title":"Fields Institute Communications","author":"Pardalos PM","year":"1998"},{"key":"e_1_2_7_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-3449-1_9"},{"key":"e_1_2_7_28_2","doi-asserted-by":"publisher","DOI":"10.1137\/S105262340139001X"},{"key":"e_1_2_7_29_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1952.tb01525.x"},{"key":"e_1_2_7_30_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.28.2.246.14485"},{"key":"e_1_2_7_31_2","doi-asserted-by":"publisher","DOI":"10.1145\/227683.227684"},{"key":"e_1_2_7_32_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107980012a"},{"key":"e_1_2_7_33_2","unstructured":"NesterovY Quality of semidefinite relaxation for nonconvex quadratic optimization. CORE Discussion Paper 9719 Belgium March1997."},{"key":"e_1_2_7_34_2","volume-title":"Probability Theory","author":"R\u00e9nyi A","year":"1970"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.781","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.781","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T02:25:41Z","timestamp":1694571941000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1002\/nla.781"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/nla.781","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,4]]}}}