{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T22:55:28Z","timestamp":1781650528569,"version":"3.54.5"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,6,5]],"date-time":"2017-06-05T00:00:00Z","timestamp":1496620800000},"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":["J Glob Optim"],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1007\/s10898-017-0538-5","type":"journal-article","created":{"date-parts":[[2017,6,5]],"date-time":"2017-06-05T05:32:10Z","timestamp":1496640730000},"page":"745-760","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Global optimization for optimal power flow over transmission networks"],"prefix":"10.1007","volume":"69","author":[{"given":"Y.","family":"Shi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0292-6061","authenticated-orcid":false,"given":"H. D.","family":"Tuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Tuy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Su","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,6,5]]},"reference":[{"issue":"8","key":"538_CR1","first-page":"431","volume":"3","author":"J Carpentier","year":"1962","unstructured":"Carpentier, J.: Contribution to the economic dispatch problem. Bull. Soc. Fr. Electr. 3(8), 431\u2013447 (1962)","journal-title":"Bull. Soc. Fr. Electr."},{"issue":"2","key":"538_CR2","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/59.76723","volume":"6","author":"M Huneault","year":"1991","unstructured":"Huneault, M., Galiana, F.D.: A survey of the optimal power flow literature. IEEE Trans. Power Syst. 6(2), 762\u2013770 (1991)","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"538_CR3","first-page":"96","volume":"14","author":"JA Momoh","year":"1999","unstructured":"Momoh, J.A., El-Hawary, M.E., Adapa, R.: A review of selected optimal power flow literature to 1993. Part I: nonlinear and quadratic programming approaches. Solar Energy 14(1), 96\u2013104 (1999)","journal-title":"Solar Energy"},{"issue":"5","key":"538_CR4","first-page":"450","volume":"4","author":"KS Pandya","year":"2008","unstructured":"Pandya, K.S., Joshi, S.K.: A survey of optimal power flow methods. J. Theor. Appl. Inf. Technol. 4(5), 450\u2013458 (2008)","journal-title":"J. Theor. Appl. Inf. Technol."},{"issue":"1","key":"538_CR5","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TPWRS.2011.2160974","volume":"27","author":"J Lavaei","year":"2012","unstructured":"Lavaei, J., Low, S.H.: Zero duality gap in optimal power flow problem. IEEE Trans. Power Syst. 27(1), 92\u2013107 (2012)","journal-title":"IEEE Trans. Power Syst."},{"issue":"4","key":"538_CR6","doi-asserted-by":"crossref","first-page":"4780","DOI":"10.1109\/TPWRS.2013.2274577","volume":"28","author":"W Bukhsh","year":"2013","unstructured":"Bukhsh, W., Grothey, A., McKinnon, K., Trodden, P.: Local solutions of the optimal power flow problem. IEEE Trans. Power Syst. 28(4), 4780\u20134788 (2013)","journal-title":"IEEE Trans. Power Syst."},{"issue":"6\u20137","key":"538_CR7","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.ijepes.2007.12.003","volume":"30","author":"X Bai","year":"2008","unstructured":"Bai, X., Wei, H., Fujisawa, K., Wang, Y.: Semidefinite programming for optimal power flow problems. Electr. Power Energy Syst. 30(6\u20137), 383\u2013392 (2008)","journal-title":"Electr. Power Energy Syst."},{"key":"538_CR8","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1007\/s10898-012-9917-0","volume":"56","author":"H Tuy","year":"2013","unstructured":"Tuy, H., Tuan, H.D.: Generalized S-lemma and strong duality in nonconvex quadratic programming. J. Glob Optim. 56, 1045\u20131072 (2013)","journal-title":"J. Glob Optim."},{"key":"538_CR9","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1109\/TPWRS.2014.2322051","volume":"30","author":"R Madani","year":"2015","unstructured":"Madani, R., Sojoudi, S., Lavaei, J.: Convex relaxation for optimal power flow problem: mesh networks. IEEE Trans. Power Syst. 30, 199\u2013211 (2015)","journal-title":"IEEE Trans. Power Syst."},{"key":"538_CR10","doi-asserted-by":"crossref","unstructured":"Madani, R., Ashraphijuo, M., Lavaei, J.: Promises of conic relaxation for contigency-constrained optimal power flow problem. IEEE Trans. Power Syst. 31(2), 1297\u20131307 (2015)","DOI":"10.1109\/TPWRS.2015.2411391"},{"issue":"1","key":"538_CR11","first-page":"463","volume":"30","author":"C Jocz","year":"2015","unstructured":"Jocz, C., Maeght, J., Panciatici, P., Gilbert, J.C.: Application of the moment-SOS approach to global optimization of the OPF problem. IEEE Trans. Power Syst. 30(1), 463\u2013470 (2015)","journal-title":"IEEE Trans. Power Syst."},{"issue":"3","key":"538_CR12","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"JB 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":"538_CR13","doi-asserted-by":"crossref","unstructured":"Tuan, H.\u00a0D., Hoang, N.\u00a0T., Ngo, H.\u00a0Q., Tuy, H., Vo, B.: A dual frequency-selective bounded real lemma and its applications to iir filter design. In: Proc. 45th IEEE Conf. Control and Decision (CDC), pp. 1478\u20131485 (2006)","DOI":"10.1109\/CDC.2006.377255"},{"issue":"6","key":"538_CR14","doi-asserted-by":"crossref","first-page":"2941","DOI":"10.1109\/TSP.2012.2189857","volume":"60","author":"HA Phan","year":"2012","unstructured":"Phan, H.A., Tuan, H.D., Kha, H.H., Ngo, D.T.: Nonsmooth optimization for efficient beamforming in cognitive radio multicast transmission. IEEE Trans. Signal Process. 60(6), 2941\u20132951 (2012)","journal-title":"IEEE Trans. Signal Process."},{"key":"538_CR15","doi-asserted-by":"crossref","unstructured":"Tuy, H.: Convex Analysis and Global Optimization, 2nd edn. Springer-Verlag (2017)","DOI":"10.1007\/978-3-319-31484-6"},{"issue":"1","key":"538_CR16","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/TPWRS.2010.2051168","volume":"26","author":"RD Zimmerman","year":"2011","unstructured":"Zimmerman, R.D., Murillo-Sanchez, C.E., Thomas, R.J.: MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26(1), 12\u201319 (2011)","journal-title":"IEEE Trans. Power Syst."},{"key":"538_CR17","volume-title":"Numerical Optimization Theoretical and Practical Aspects","author":"JF Bonnans","year":"2006","unstructured":"Bonnans, J.F., Gilbert, J.C., Lemarechal, C., Sagastiza bal, C.: Numerical Optimization Theoretical and Practical Aspects, 2nd edn. Springer, Berlin (2006)","edition":"2"},{"issue":"4","key":"538_CR18","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1287\/opre.26.4.681","volume":"26","author":"BR Marks","year":"1978","unstructured":"Marks, B.R., Wright, G.P.: A general inner approximation algorithm for nonconvex mathematical programms. Oper. Res. 26(4), 681\u2013683 (1978)","journal-title":"Oper. Res."},{"key":"538_CR19","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1080\/002071700219803","volume":"73","author":"HD Tuan","year":"2000","unstructured":"Tuan, H.D., Apkarian, P., Hosoe, S., Tuy, H.: D.c. optimization approach to robust controls: the feasibility problems. Int. J. Control 73, 89\u2013104 (2000)","journal-title":"Int. J. Control"},{"issue":"2","key":"538_CR20","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1109\/TWC.2011.120911.110139","volume":"11","author":"HH Kha","year":"2012","unstructured":"Kha, H.H., Tuan, H.D., Nguyen, H.H.: Fast global optimal power allocation in wireless networks by local d.c. programming. IEEE Trans. Wirel. Commun. 11(2), 510\u2013515 (2012)","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"104","key":"538_CR21","first-page":"23","volume":"133","author":"LTH An","year":"2005","unstructured":"An, L.T.H., Tao, P.D.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133(104), 23\u201345 (2005)","journal-title":"Ann. Oper. Res."},{"key":"538_CR22","volume-title":"Convex Analysis and Minimization Algorithms","author":"JB Hiriart-Urruty","year":"1996","unstructured":"Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms, 2nd edn. Springer, Berlin (1996)","edition":"2"},{"key":"538_CR23","doi-asserted-by":"crossref","unstructured":"Lofberg, J.: Yalmip: a toolbox for modeling and optimization in matlab. In: IEEE Inter, pp. 284\u2013289. Sept, Symp. on Computer Aided Control Systems Design (2004)","DOI":"10.1109\/CACSD.2004.1393890"},{"key":"538_CR24","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/10556789908805766","volume":"11","author":"JF Sturm","year":"1999","unstructured":"Sturm, J.F.: Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. 11, 625\u2013653 (1999)","journal-title":"Optim. Methods Softw."},{"key":"538_CR25","unstructured":"Bukhsh, W., Grothey, A., McKinnon, K., Trodden, P.: Test case archive of optimal power flow (OPF) problems with local optima. http:\/\/www.maths.ed.ac.uk\/optenergy\/LocalOpt\/introduction.html"},{"issue":"11","key":"538_CR26","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.1109\/TAC.2008.2007156","volume":"53","author":"HG Hoang","year":"2008","unstructured":"Hoang, H.G., Tuan, H.D., Apkarian, P.: A Lyapunov variable-free KYP lemma for SISO continuous systems. IEEE Trans. Autom. Control 53(11), 2669\u20132673 (2008)","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-017-0538-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-017-0538-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-017-0538-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T12:14:03Z","timestamp":1569413643000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-017-0538-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,5]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["538"],"URL":"https:\/\/doi.org\/10.1007\/s10898-017-0538-5","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,5]]}}}