{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:20:53Z","timestamp":1740122453097,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,5,24]],"date-time":"2015-05-24T00:00:00Z","timestamp":1432425600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100005989","name":"Ministrstvo za Izobra\u017eevanje, Znanost in \u0160port","doi-asserted-by":"publisher","award":["ID0EXIAE64"],"award-info":[{"award-number":["ID0EXIAE64"]}],"id":[{"id":"10.13039\/501100005989","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["ID0EQMAE65"],"award-info":[{"award-number":["ID0EQMAE65"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Marsden Fund Council of the Royal Society","award":["ID0EJQAE66"],"award-info":[{"award-number":["ID0EJQAE66"]}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["ID0ENRAE67"],"award-info":[{"award-number":["ID0ENRAE67"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2016,2]]},"DOI":"10.1007\/s10898-015-0308-1","type":"journal-article","created":{"date-parts":[[2015,5,23]],"date-time":"2015-05-23T04:47:42Z","timestamp":1432356462000},"page":"325-348","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Constrained trace-optimization of polynomials in freely noncommuting variables"],"prefix":"10.1007","volume":"64","author":[{"given":"Igor","family":"Klep","sequence":"first","affiliation":[]},{"given":"Janez","family":"Povh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,5,24]]},"reference":[{"key":"308_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-0769-0","volume-title":"Handbook of Semidefinite, Conic and Polynomial Optimization: Theory, Algorithms, Software and Applications, volume 166 of International Series in Operational Research and Management Science","author":"MF Anjos","year":"2012","unstructured":"Anjos, M.F., Lasserre, J.B.: Handbook of Semidefinite, Conic and Polynomial Optimization: Theory, Algorithms, Software and Applications, volume 166 of International Series in Operational Research and Management Science. Springer, Berlin (2012)"},{"key":"308_CR2","volume-title":"A Course in Convexity, Volume 54 of Graduate Studies in Mathematics","author":"A Barvinok","year":"2002","unstructured":"Barvinok, A.: A Course in Convexity, Volume 54 of Graduate Studies in Mathematics. American Mathematical Society, Providence (2002)"},{"issue":"1\u20132","key":"308_CR3","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s10107-011-0505-8","volume":"137","author":"S Burgdorf","year":"2013","unstructured":"Burgdorf, S., Cafuta, K., Klep, I., Povh, J.: The tracial moment problem and trace-optimization of polynomials. Math. Program. 137(1\u20132), 557\u2013578 (2013)","journal-title":"Math. Program."},{"issue":"4","key":"308_CR4","doi-asserted-by":"crossref","first-page":"605","DOI":"10.4310\/MRL.2009.v16.n4.a5","volume":"16","author":"M Bre\u0161ar","year":"2009","unstructured":"Bre\u0161ar, M., Klep, I.: Noncommutative polynomials, Lie skew-ideals and tracial Nullstellens\u00e4tze. Math. Res. Lett. 16(4), 605\u2013626 (2009)","journal-title":"Math. Res. Lett."},{"key":"308_CR5","first-page":"141","volume":"68","author":"S Burgdorf","year":"2012","unstructured":"Burgdorf, S., Klep, I.: The truncated tracial moment problem. J. Oper. Theory 68, 141\u2013163 (2012)","journal-title":"J. Oper. Theory"},{"issue":"2","key":"308_CR6","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.aim.2010.08.003","volume":"226","author":"P Br\u00e4nd\u00e9n","year":"2011","unstructured":"Br\u00e4nd\u00e9n, P.: Obstructions to determinantal representability. Adv. Math. 226(2), 1202\u20131212 (2011)","journal-title":"Adv. Math."},{"issue":"568","key":"308_CR7","first-page":"x+52","volume":"119","author":"RE Curto","year":"1996","unstructured":"Curto, R.E., Fialkow, L.A.: Solution of the truncated complex moment problem for flat data. Mem. Am. Math. Soc. 119(568), x+52 (1996)","journal-title":"Mem. Am. Math. Soc."},{"issue":"648","key":"308_CR8","first-page":"x+56","volume":"136","author":"RE Curto","year":"1998","unstructured":"Curto, R.E., Fialkow, L.A.: Flat extensions of positive moment matrices: recursively generated relations. Mem. Am. Math. Soc. 136(648), x+56 (1998)","journal-title":"Mem. Am. Math. Soc."},{"issue":"2","key":"308_CR9","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/j.jmaa.2010.03.045","volume":"369","author":"J Cimpri\u010d","year":"2010","unstructured":"Cimpri\u010d, J.: A method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programming. J. Math. Anal. Appl. 369(2), 443\u2013452 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"308_CR10","doi-asserted-by":"crossref","unstructured":"Cafuta, K., Klep, I., Povh, J.: NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials. Optim. Methods Softw., 26(3), 363\u2013380 (2011). Available from http:\/\/ncsostools.fis.unm.si\/","DOI":"10.1080\/10556788.2010.544312"},{"issue":"2","key":"308_CR11","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1137\/110830733","volume":"22","author":"K Cafuta","year":"2012","unstructured":"Cafuta, K., Klep, I., Povh, J.: Constrained polynomial optimization problems with noncommuting variables. SIAM J. Optim. 22(2), 363\u2013383 (2012)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"308_CR12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.2307\/1971057","volume":"104","author":"A Connes","year":"1976","unstructured":"Connes, A.: Classification of injective factors. Cases $$II_{1}, II_{\\infty }, III_{\\lambda }, \\lambda \\ne 1$$ I I 1 , I I \u221e , I I I \u03bb , \u03bb \u2260 1 . Ann. Math. (2) 104(1), 73\u2013115 (1976)","journal-title":"Ann. Math. (2)"},{"key":"308_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/b105286","volume-title":"Aspects of Semidefinite Programming, Volume 65 of Applied Optimization","author":"E Klerk de","year":"2002","unstructured":"de Klerk, E.: Aspects of Semidefinite Programming, Volume 65 of Applied Optimization. Kluwer, Dordrecht (2002)"},{"issue":"1","key":"308_CR14","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.aim.2012.04.028","volume":"231","author":"JW Helton","year":"2012","unstructured":"Helton, J.W., Klep, I., McCullough, S.: The convex Positivstellensatz in a free algebra. Adv. Math. 231(1), 516\u2013534 (2012)","journal-title":"Adv. Math."},{"key":"308_CR15","doi-asserted-by":"crossref","unstructured":"Henrion, D., Lasserre, J.B., L\u00f6fberg, J.: GloptiPoly 3: moments, optimization and semidefinite programming. Optim. Methods Softw., 24(4\u20135), 761\u2013779 (2009). Available from http:\/\/www.laas.fr\/henrion\/software\/gloptipoly3\/","DOI":"10.1080\/10556780802699201"},{"issue":"9","key":"308_CR16","doi-asserted-by":"crossref","first-page":"3721","DOI":"10.1090\/S0002-9947-04-03433-6","volume":"356","author":"JW Helton","year":"2004","unstructured":"Helton, J.W., McCullough, S.: A Positivstellensatz for non-commutative polynomials. Trans. Am. Math. Soc. 356(9), 3721\u20133737 (2004)","journal-title":"Trans. Am. Math. Soc."},{"issue":"2","key":"308_CR17","doi-asserted-by":"crossref","first-page":"979","DOI":"10.4007\/annals.2012.176.2.6","volume":"176","author":"JW Helton","year":"2012","unstructured":"Helton, J.W., McCullough, S.: Every convex free basic semi-algebraic set has an LMI representation. Ann. Math. (2) 176(2), 979\u20131013 (2012)","journal-title":"Ann. Math. (2)"},{"key":"308_CR18","unstructured":"Helton, J.W., McCullough, S., de Oliveira, M.C., Putinar, M.: Engineering systems and free semi-algebraic geometry. In: Emerging Applications of Algebraic Geometry, Volume 149 of IMA Vol. Math. Appl., pp. 17\u201362. Springer, (2008)"},{"issue":"4","key":"308_CR19","doi-asserted-by":"crossref","first-page":"1816","DOI":"10.1016\/j.aim.2007.09.016","volume":"217","author":"I Klep","year":"2008","unstructured":"Klep, I., Schweighofer, M.: Connes\u2019 embedding conjecture and sums of Hermitian squares. Adv. Math. 217(4), 1816\u20131837 (2008)","journal-title":"Adv. Math."},{"key":"308_CR20","doi-asserted-by":"crossref","unstructured":"Kaliuzhnyi-Verbovetskyi, D.S., Vinnikov, V.: Foundations of free noncommutative function theory, volume 199. American Mathematical Society, (2014)","DOI":"10.1090\/surv\/199"},{"key":"308_CR21","doi-asserted-by":"crossref","unstructured":"Lasserre, J.B.: Global optimization with polynomials and the problem of moments. J. Optim. 11(3), 796\u2013817 (2000\/2001)","DOI":"10.1137\/S1052623400366802"},{"key":"308_CR22","doi-asserted-by":"crossref","DOI":"10.1142\/p665","volume-title":"Moments, Positive Polynomials and Their Applications","author":"JB Lasserre","year":"2009","unstructured":"Lasserre, J.B.: Moments, Positive Polynomials and Their Applications, vol. 1. Imperial College Press, London (2009)"},{"key":"308_CR23","doi-asserted-by":"crossref","unstructured":"Laurent, M.: Sums of squares, moment matrices and optimization over polynomials. In: Emerging Applications of Algebraic Geometry, pp. 157\u2013270. Springer, (2009)","DOI":"10.1007\/978-0-387-09686-5_7"},{"key":"308_CR24","unstructured":"L\u00f6fberg, J.: YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004. Available from http:\/\/control.ee.ethz.ch\/joloef\/wiki\/pmwiki.php"},{"key":"308_CR25","unstructured":"Mittelmann, D.: An independent benchmarking of SDP and SOCP solvers. Math. Program. B, 95, 407\u2013430 (2003). http:\/\/plato.asu.edu\/bench.html"},{"issue":"1","key":"308_CR26","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1137\/070704575","volume":"20","author":"J Malick","year":"2009","unstructured":"Malick, J., Povh, J., Rendl, F., Wiegele, A.: Regularization methods for semidefinite programming. SIAM J. Optim. 20(1), 336\u2013356 (2009)","journal-title":"SIAM J. Optim."},{"issue":"6","key":"308_CR27","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1007\/s10208-014-9225-9","volume":"14","author":"J Nie","year":"2014","unstructured":"Nie, J.: The $${\\cal A}$$ A -truncated $${\\cal K}$$ K -moment problem. Found. Comput. Math. 14(6), 1243\u20131276 (2014)","journal-title":"Found. Comput. Math."},{"key":"308_CR28","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1007\/s00454-014-9598-1","volume":"51","author":"T Netzer","year":"2014","unstructured":"Netzer, T., Thom, A.: Hyperbolic polynomials and generalized Clifford algebras. Disc. Comput. Geom. 51, 802\u2013814 (2014)","journal-title":"Disc. Comput. Geom."},{"issue":"5","key":"308_CR29","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1137\/090760155","volume":"20","author":"S Pironio","year":"2010","unstructured":"Pironio, S., Navascu\u00e9s, M., Ac\u00edn, A.: Convergent relaxations of polynomial optimization problems with noncommuting variables. SIAM J. Optim. 20(5), 2157\u20132180 (2010)","journal-title":"SIAM J. Optim."},{"key":"308_CR30","unstructured":"Prajna, S., Papachristodoulou, A., Seiler, P., Parrilo, P.A.: SOSTOOLS and its control applications. In: Positive polynomials in control, Volume 312 of Lecture Notes in Control and Inform. Sci., pp. 273\u2013292. Springer, Berlin, (2005)"},{"issue":"3","key":"308_CR31","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/0001-8708(76)90027-X","volume":"19","author":"C Procesi","year":"1976","unstructured":"Procesi, C.: The invariant theory of $$n\\times n$$ n \u00d7 n matrices. Adv. Math. 19(3), 306\u2013381 (1976)","journal-title":"Adv. Math."},{"issue":"3","key":"308_CR32","doi-asserted-by":"crossref","first-page":"395","DOI":"10.2307\/1970962","volume":"104","author":"C Procesi","year":"1976","unstructured":"Procesi, C., Schacher, M.: A non-commutative real nullstellensatz and hilbert\u2019s 17th problem. Ann. Math. 104(3), 395\u2013406 (1976)","journal-title":"Ann. Math."},{"issue":"1","key":"308_CR33","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1515\/advg.2001.005","volume":"1","author":"V Powers","year":"2001","unstructured":"Powers, V., Scheiderer, C.: The moment problem for non-compact semialgebraic sets. Adv. Geom. 1(1), 71\u201388 (2001)","journal-title":"Adv. Geom."},{"issue":"3","key":"308_CR34","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1512\/iumj.1993.42.42045","volume":"42","author":"M Putinar","year":"1993","unstructured":"Putinar, M.: Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42(3), 969\u2013984 (1993)","journal-title":"Indiana Univ. Math. J."},{"key":"308_CR35","volume-title":"Polynomial Identities in Ring Theory Volume 84 of Pure and Applied Mathematics","author":"LH Rowen","year":"1980","unstructured":"Rowen, L.H.: Polynomial Identities in Ring Theory Volume 84 of Pure and Applied Mathematics, vol. 84. Academic Press Inc., New York (1980)"},{"key":"308_CR36","doi-asserted-by":"crossref","unstructured":"Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw., 11\/12(1\u20134), 625\u2013653 (1999). Available from http:\/\/sedumi.ie.lehigh.edu\/","DOI":"10.1080\/10556789908805766"},{"key":"308_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-10453-8","volume-title":"Theory of Operator Algebras. III","author":"M Takesaki","year":"2003","unstructured":"Takesaki, M.: Theory of Operator Algebras. III. Springer, Berlin (2003)"},{"key":"308_CR38","doi-asserted-by":"crossref","unstructured":"Toh, K.C., Todd, M.J., T\u00fct\u00fcnc\u00fc, R.H.: SDPT3\u2014a MATLAB software package for semidefinite programming, version 1.3. Optim. Methods Softw., 11\/12(1\u20134), 545\u2013581 (1999). Available from http:\/\/www.math.nus.edu.sg\/mattohkc\/sdpt3.html","DOI":"10.1080\/10556789908805762"},{"issue":"1","key":"308_CR39","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L Vandenberghe","year":"1996","unstructured":"Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Rev. 38(1), 49\u201395 (1996)","journal-title":"SIAM Rev."},{"key":"308_CR40","doi-asserted-by":"crossref","unstructured":"Waki, H., Kim, S., Kojima, M., Muramatsu, M., Sugimoto, H.: Algorithm 883: sparsePOP\u2014a sparse semidefinite programming relaxation of polynomial optimization problems. ACM Trans. Math. Software, 35(2), Art. 15, 13 (2009)","DOI":"10.1145\/1377612.1377619"},{"key":"308_CR41","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-4381-7","volume-title":"Handbook of Semidefinite Programming","author":"H Wolkowicz","year":"2000","unstructured":"Wolkowicz, H., Saigal, R., Vandenberghe, L.: Handbook of Semidefinite Programming. Kluwer, Dordrecht (2000)"},{"issue":"12","key":"308_CR42","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1080\/00207720802300370","volume":"39","author":"S Xu","year":"2008","unstructured":"Xu, S., Lam, J.: A survey of linear matrix inequality techniques in stability analysis of delay systems. Int. J. Syst. Sci. 39(12), 1095\u20131113 (2008)","journal-title":"Int. J. Syst. Sci."},{"key":"308_CR43","doi-asserted-by":"crossref","unstructured":"Yamashita, M., Fujisawa, K., Kojima, M.: Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0). Optim. Methods Softw., 18(4), 491\u2013505 (2003). Available from http:\/\/sdpa.sourceforge.net\/","DOI":"10.1080\/1055678031000118482"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0308-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-015-0308-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0308-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,25]],"date-time":"2019-08-25T09:25:46Z","timestamp":1566725146000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-015-0308-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,24]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["308"],"URL":"https:\/\/doi.org\/10.1007\/s10898-015-0308-1","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2015,5,24]]}}}