{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T21:16:33Z","timestamp":1776287793639,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,11,5]],"date-time":"2015-11-05T00:00:00Z","timestamp":1446681600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2016,7]]},"DOI":"10.1007\/s11075-015-0058-7","type":"journal-article","created":{"date-parts":[[2015,11,5]],"date-time":"2015-11-05T01:10:15Z","timestamp":1446685815000},"page":"539-604","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Barzilai and Borwein\u2019s method for multiobjective optimization problems"],"prefix":"10.1007","volume":"72","author":[{"given":"Vahid","family":"Morovati","sequence":"first","affiliation":[]},{"given":"Latif","family":"Pourkarimi","sequence":"additional","affiliation":[]},{"given":"Hadi","family":"Basirzadeh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,5]]},"reference":[{"key":"58_CR1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal 8, 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal"},{"key":"58_CR2","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s001860000043","volume":"51","author":"J Fliege","year":"2000","unstructured":"Fliege, J., Svaiter, B.F.: Steepest descent methods for multicriteria optimization. Math. Methods Oper. Res. 51, 479\u2013494 (2000)","journal-title":"Math. Methods Oper. Res."},{"key":"58_CR3","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/B:COAP.0000018877.86161.8b","volume":"28","author":"LM Gra\u00f1a Drummond","year":"2004","unstructured":"Gra\u00f1a Drummond, L.M.: A projected gradient method for vector optimization problems. Comput. Optim. Appl. 28, 5\u201329 (2004)","journal-title":"Comput. Optim. Appl."},{"key":"58_CR4","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.cam.2004.06.018","volume":"175","author":"LMG Drummond","year":"2005","unstructured":"Drummond, L.M.G., Svaiter, B.F.: A steepest descent method for vector optimization. J. Comput. Appl. Math. 175, 395\u2013414 (2005)","journal-title":"J. Comput. Appl. Math."},{"key":"58_CR5","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1137\/08071692X","volume":"20","author":"J Fliege","year":"2009","unstructured":"Fliege, J., Drummond, L.M.G., Svaiter, B.F.: Newton\u2019s method for multiobjective optimization. SIAM J. Optim. 20, 602\u2013626 (2009)","journal-title":"SIAM J. Optim."},{"key":"58_CR6","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.orl.2011.07.008","volume":"39","author":"S Qu","year":"2011","unstructured":"Qu, S., Goh, M., Chan, F.T.S.: Quasi-Newton methods for solving multiobjective optimization. Oper. Res. Lett. 39, 397\u2013399 (2011)","journal-title":"Oper. Res. Lett."},{"key":"58_CR7","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1016\/j.cam.2013.06.045","volume":"255","author":"Z Povalej","year":"2014","unstructured":"Povalej, Z.: Quasi-Newton\u2019s method for multiobjective optimization. J. Comput. Appl. Math. 255, 765\u2013777 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"58_CR8","unstructured":"Qu, S., Goh, M., Liang, B.: Trust region methods for solving multiobjective optimisation. Optim Method Softw, iFirst, 1\u201316 (2012)"},{"key":"58_CR9","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1007\/s10957-013-0392-7","volume":"160","author":"KDV Villacorta","year":"2014","unstructured":"Villacorta, K.D.V., Oliveira, P.R., Soubeyran, A.: A trust-region method for unconstrained multiobjective problems with applications in satisficing processes. J. Optim. Theory Appl. 160, 865\u2013889 (2014)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"58_CR10","first-page":"544","volume":"10","author":"A Sayadi Bander","year":"2015","unstructured":"Sayadi Bander, A., Morovati, V., Basirzadeh, H.: A super non-dominated point for multi-objective transportation problem. Appl. Appl. Math 10(1), 544\u2013551 (2015)","journal-title":"Appl. Appl. Math"},{"key":"58_CR11","doi-asserted-by":"crossref","first-page":"157","DOI":"10.22436\/jmcs.010.03.01","volume":"10","author":"H Basirzadeh","year":"2014","unstructured":"Basirzadeh, H., Morovati, V., Sayadi, A.: A quick method to calculate the super-efficient point in multi-objective assignment problems. J. Math. Comput. Sci. 10, 157\u2013162 (2014)","journal-title":"J. Math. Comput. Sci."},{"key":"58_CR12","doi-asserted-by":"crossref","DOI":"10.1002\/0471787779","volume-title":"Nonlinear Programming: Theory and Algorithms","author":"MS Bazaraa","year":"2006","unstructured":"Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms. Wiley, New Jersey (2006)"},{"key":"58_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-79159-1","volume-title":"Adaptive Scalarization Methods in Multiobjective Optimization","author":"Eichfelder. G.","year":"2008","unstructured":"Eichfelder. G.: Adaptive Scalarization Methods in Multiobjective Optimization. Springer, Berlin (2008)"},{"key":"58_CR14","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/S1052623496307510","volume":"8","author":"I Das","year":"1998","unstructured":"Das, I., Dennis, J.E.: Normal-boundary intersection: A new method for generating Pareto optimal points in nonlinear multicriteria optimization problems. SIAM J. Optim. 8, 631\u2013657 (1998)","journal-title":"SIAM J. Optim."},{"key":"58_CR15","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1162\/evco.1999.7.3.205","volume":"7","author":"K Deb","year":"1999","unstructured":"Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Evol. Comut. 7, 205\u2013230 (1999)","journal-title":"Evol. Comut."},{"key":"58_CR16","volume-title":"Multicriteria Optimization","author":"M Ehrgott","year":"2005","unstructured":"Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2005)"},{"key":"58_CR17","doi-asserted-by":"crossref","unstructured":"Hillermeier, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. ISNM 25, Berlin (2001)","DOI":"10.1007\/978-3-0348-8280-4"},{"key":"58_CR18","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/11844297_52","volume-title":"Proceedings of the Ninth International Conference on Parallel Problem Solving from Nature (PPSN IX)","author":"M Preuss","year":"2006","unstructured":"Preuss, M., Naujoks, B., Rudolph, G.: Pareto set and EMOA behavior for simple multimodal multiobjective functions. In: Runarsson, T.P., et al. (eds.) Proceedings of the Ninth International Conference on Parallel Problem Solving from Nature (PPSN IX), pp 513\u2013522. Springer, Berlin (2006)"},{"key":"58_CR19","unstructured":"Stadtler, W., Dauer, J.: Multicriteria Optimization in Engineering: A Tutorial and Survey. AIAA (1992)"},{"key":"58_CR20","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1162\/106365600568202","volume":"8","author":"E Zitzler","year":"2000","unstructured":"Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comut. 8, 173\u2013195 (2000)","journal-title":"Evol. Comut."},{"key":"58_CR21","volume-title":"Vektoroptimierung: theorie, verfahren und anwendungen","author":"A Gopfert","year":"1990","unstructured":"Gopfert, A., Nehse, R.: Vektoroptimierung: theorie, verfahren und anwendungen. B. G. Teubner Verlag, Leipzig (1990)"},{"key":"58_CR22","volume-title":"Theory of Vector Optimization","author":"DT Luc","year":"1988","unstructured":"Luc, D.T.: Theory of Vector Optimization. Springer-Verlag, Berlin (1988)"},{"key":"58_CR23","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1162\/106365602760234108","volume":"10","author":"M Laumanns","year":"2002","unstructured":"Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comut. 10, 263\u2013282 (2002)","journal-title":"Evol. Comut."},{"issue":"7","key":"58_CR24","doi-asserted-by":"crossref","first-page":"881","DOI":"10.2514\/2.7537","volume":"37","author":"RV Tappeta","year":"1999","unstructured":"Tappeta, R.V., Renaud, J.E.: Interactive multiobjective optimization procedure. AIAA J. 37(7), 881\u2013889 (1999)","journal-title":"AIAA J."},{"key":"58_CR25","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1137\/1019005","volume":"19","author":"JE Dennis","year":"1977","unstructured":"Dennis, J.E., More, J.J.: Quasi-Newton methods, motivation and theory. SIAM Rev. 19, 46\u201389 (1977)","journal-title":"SIAM Rev."},{"key":"58_CR26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/22.1.1","volume":"22","author":"YH Dai","year":"2002","unstructured":"Dai, Y.H., Liao, L.Z.: R-Linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 22, 1\u201310 (2002)","journal-title":"IMA J. Numer. Anal."},{"key":"58_CR27","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971200","volume-title":"Numerical Methods for Unconstrained Nonlinear Equations","author":"JE Dennis","year":"1996","unstructured":"Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Nonlinear Equations. SIAM, Philadelphia (1996)"},{"key":"58_CR28","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1023\/A:1022614029984","volume":"96","author":"E Carrizosa","year":"1998","unstructured":"Carrizosa, E., Frenk, J.B.G.: Dominating sets for convex functions with some application. J. Optim. Theory Appl. 96, 281\u2013295 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"58_CR29","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s00158-004-0465-1","volume":"29","author":"IY Kim","year":"2005","unstructured":"Kim, I.Y., De Weck, O.L.: Adaptive weighted sum method for bi-objective optimization: Pareto front generation. Struct. Multidicip. O 29, 149\u2013158 (2005)","journal-title":"Struct. Multidicip. O"},{"key":"58_CR30","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., More, J.J.: Benchmarking optimization software with performance profiles. Math. Program 91, 201\u2013213 (2002)","journal-title":"Math. Program"},{"issue":"3","key":"58_CR31","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1137\/10079731X","volume":"21","author":"AL Custodio","year":"2011","unstructured":"Custodio, A.L., Madeira, J.F.A., Vaz, A.I.F., Vicente, L.N.: Direct multisearch for multiobjective optimization. SIAM J. Optim. 21(3), 1109\u20131140 (2011)","journal-title":"SIAM J. Optim."},{"issue":"5","key":"58_CR32","doi-asserted-by":"crossref","first-page":"2088","DOI":"10.1109\/TSMCB.2004.834438","volume":"34","author":"S Bandyopadhyay","year":"2004","unstructured":"Bandyopadhyay, S., Pal, S.K., Aruna, B.: Multiobjective GAs, quantitative indices, and pattern classification. IEEE Trans. Syst. Man Cybern. B Cybern. 34(5), 2088\u20132099 (2004)","journal-title":"IEEE Trans. Syst. Man Cybern. B Cybern."},{"issue":"2","key":"58_CR33","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","volume":"7","author":"E Zitzler","year":"2003","unstructured":"Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans. Evol. Comput. 7(2), 117\u2013132 (2003)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"58_CR34","unstructured":"Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. TIK Report 214, Computer Engineering and Networks Laboratory, ETH Zurich (2006)"},{"key":"58_CR35","unstructured":"Jin, Y., Olhofer, M., Sendhoff, B.: Dynamic weighted aggregation for evolutionary multiobjective optimization: Why does it work and how? In: Proceedings of the Genetic and Evolutionary Computation Conference, pp 1042\u20131049 (2001)"},{"key":"58_CR36","doi-asserted-by":"crossref","unstructured":"Fu, Y., Diwekar, U.M.: An efficient sampling approach to multiobjective optimization. Ann. Oper. Res. 132, 109\u2013134 (2004)","DOI":"10.1023\/B:ANOR.0000045279.46948.dd"},{"issue":"5","key":"58_CR37","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1115\/1.1904639","volume":"127","author":"S Shan","year":"2005","unstructured":"Shan, S., Wang, G.G.: An efficient pareto set identification approach for multiobjective optimization on black-box functions. J. Mech. Des. 127(5), 866\u2013874 (2005)","journal-title":"J. Mech. Des."},{"key":"58_CR38","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1287\/mnsc.30.11.1268","volume":"30","author":"G Evans","year":"1984","unstructured":"Evans, G.: Overview of techniques for solving multiobjective mathematical programs. Manag. Sci. 30, 1268\u20131282 (1984)","journal-title":"Manag. Sci."},{"key":"58_CR39","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/S0377-2217(97)00056-8","volume":"105","author":"DJ White","year":"1998","unstructured":"White, D.J.: Epsilon-dominating solutions in mean-variance portfolio analysis. European J. Oper. Res. 105, 457\u2013466 (1998)","journal-title":"European J. Oper. Res."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-0058-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-015-0058-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-0058-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T04:18:58Z","timestamp":1567311538000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-015-0058-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,5]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["58"],"URL":"https:\/\/doi.org\/10.1007\/s11075-015-0058-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,5]]}}}