{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T07:06:43Z","timestamp":1747638403901,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T00:00:00Z","timestamp":1602720000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T00:00:00Z","timestamp":1602720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100007569","name":"Carl-Zeiss-Stiftung","doi-asserted-by":"publisher","award":["Promotionsstipendium 2017-2019"],"award-info":[{"award-number":["Promotionsstipendium 2017-2019"]}],"id":[{"id":"10.13039\/100007569","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["RTG 1567"],"award-info":[{"award-number":["RTG 1567"]}],"id":[{"id":"10.13039\/501100001659","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":[[2021,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b1<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b1<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>BB method fails, i.e., it terminates without ever finding a feasible solution.<\/jats:p>","DOI":"10.1007\/s10898-020-00956-2","type":"journal-article","created":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T15:02:22Z","timestamp":1602774142000},"page":"31-61","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonconvex constrained optimization by a filtering branch and bound"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1938-6316","authenticated-orcid":false,"given":"Gabriele","family":"Eichfelder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9119-0732","authenticated-orcid":false,"given":"Kathrin","family":"Klamroth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5413-2234","authenticated-orcid":false,"given":"Julia","family":"Niebling","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,10,15]]},"reference":[{"issue":"9","key":"956_CR1","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.1016\/S0098-1354(98)00027-1","volume":"22","author":"CS Adjiman","year":"1998","unstructured":"Adjiman, C.S., Dallwig, S., Floudas, C.A., Neumaier, A.: A global optimization method, $$\\alpha $$BB, for general twice-differentiable constrained NLPs: I\u2014theoretical advances. Comput. Chem. Eng. 22(9), 1137\u20131158 (1998)","journal-title":"Comput. Chem. Eng."},{"issue":"1","key":"956_CR2","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s10589-017-9955-0","volume":"71","author":"EF Campana","year":"2018","unstructured":"Campana, E.F., Diez, M., Liuzzi, G., Lucidi, S., Pellegrini, R., Piccialli, V., Rinaldi, F., Serani, A.: A multi-objective DIRECT algorithm for ship hull optimization. Comput. Optim. Appl. 71(1), 53\u201372 (2018)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"956_CR3","doi-asserted-by":"publisher","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. Comput. 7(3), 205\u2013230 (1999)","journal-title":"Evol. Comput."},{"issue":"2","key":"956_CR4","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 181\u2013197 (2002)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"956_CR5","doi-asserted-by":"crossref","unstructured":"Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation. CEC\u201902 (Cat. No. 02TH8600), vol.\u00a01, pp. 825\u2013830 (2002)","DOI":"10.1109\/CEC.2002.1007032"},{"key":"956_CR6","volume-title":"Multicriteria Optimisation","author":"M Ehrgott","year":"2005","unstructured":"Ehrgott, M.: Multicriteria Optimisation, 2nd edn. Springer-Verlag, Berlin (2005)","edition":"2"},{"issue":"3","key":"956_CR7","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s10898-010-9588-7","volume":"50","author":"M Ehrgott","year":"2011","unstructured":"Ehrgott, M., Shao, L., Sch\u00f6bel, A.: An approximation algorithm for convex multi-objective programming problems. J. Global Optim. 50(3), 397\u2013416 (2011)","journal-title":"J. Global Optim."},{"key":"956_CR8","doi-asserted-by":"crossref","unstructured":"Eichfelder, G., Klamroth, K., Niebling, J.: Using a B&B algorithm from multiobjective optimization to solve constrained optimization problems. In: AIP Conference Proceedings, vol.\u00a02070, p.\u00a0020028 (2019)","DOI":"10.1063\/1.5089995"},{"issue":"5","key":"956_CR9","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1080\/10556788.2013.854357","volume":"29","author":"YG Evtushenko","year":"2014","unstructured":"Evtushenko, Y.G., Posypkin, M.A.: A deterministic algorithm for global multi-objective optimization. Optim. Methods Softw. 29(5), 1005\u20131019 (2014)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"956_CR10","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s10589-007-9135-8","volume":"42","author":"J Fern\u00e1ndez","year":"2009","unstructured":"Fern\u00e1ndez, J., T\u00f3th, B.: Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods. Comput. Optim. Appl. 42(3), 393\u2013419 (2009)","journal-title":"Comput. Optim. Appl."},{"key":"956_CR11","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s101070100244","volume":"91","author":"R Fletcher","year":"2002","unstructured":"Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91, 239\u2013269 (2002)","journal-title":"Math. Program."},{"key":"956_CR12","unstructured":"Fletcher, R., Leyffer, S., Toint, P.L.: A brief history of filter methods. Technical Report ANL\/MCS-P1372-0906 (2006)"},{"key":"956_CR13","doi-asserted-by":"crossref","unstructured":"Fonseca, C., Fleming, P.: Multiobjective genetic algorithms made easy: selection sharing and mating restriction. In: Proceedings of the 1st International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, pp. 45\u201352. IEEE Press (1995)","DOI":"10.1049\/cp:19951023"},{"key":"956_CR14","unstructured":"GAMS Development Corporation. General Algebraic Modeling System (GAMS) Release 24.1.3. Washington, DC, USA (2013)"},{"issue":"2","key":"956_CR15","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s00186-016-0547-z","volume":"84","author":"C G\u00fcnther","year":"2016","unstructured":"G\u00fcnther, C., Tammer, C.: Relationships between constrained and unconstrained multi-objective optimization and application in location theory. Math. Methods Oper. Res. 84(2), 359\u2013387 (2016)","journal-title":"Math. Methods Oper. Res."},{"key":"956_CR16","volume-title":"Applied Nonlinear Programming","author":"DM Himmelblau","year":"1972","unstructured":"Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill, New York (1972)"},{"issue":"2","key":"956_CR17","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1007\/s11750-015-0387-7","volume":"23","author":"P Kirst","year":"2015","unstructured":"Kirst, P., Stein, O., Steuermann, P.: Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints. TOP 23(2), 591\u2013616 (2015)","journal-title":"TOP"},{"issue":"3","key":"956_CR18","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s10898-006-9052-x","volume":"37","author":"K Klamroth","year":"2007","unstructured":"Klamroth, K., Tind, J.: Constrained optimization using multiple objective programming. J. Global Optim. 37(3), 325\u2013355 (2007)","journal-title":"J. Global Optim."},{"issue":"4","key":"956_CR19","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1007\/s10898-013-0136-0","volume":"60","author":"A L\u00f6hne","year":"2014","unstructured":"L\u00f6hne, A., Rudloff, B., Ulus, F.: Primal and dual approximation algorithms for convex vector optimization problems. J. Global Optim. 60(4), 713\u2013736 (2014)","journal-title":"J. Global Optim."},{"issue":"2","key":"956_CR20","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/BF01096720","volume":"4","author":"CD Maranas","year":"1994","unstructured":"Maranas, C.D., Floudas, C.A.: Global minimum potential energy conformations of small molecules. J. Global Optim. 4(2), 135\u2013170 (1994)","journal-title":"J. Global Optim."},{"issue":"3","key":"956_CR21","doi-asserted-by":"publisher","first-page":"934","DOI":"10.1016\/j.ejor.2016.05.045","volume":"260","author":"B Martin","year":"2016","unstructured":"Martin, B., Goldsztejn, A., Granvilliers, L., Jermann, C.: Constraint propagation using dominance in interval branch & bound for nonlinear biobjective optimization. Eur. J. Oper. Res. 260(3), 934\u2013948 (2016)","journal-title":"Eur. J. Oper. Res."},{"key":"956_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5563-6","volume-title":"Nonlinear Multiobjective Optimization","author":"K Miettinen","year":"1998","unstructured":"Miettinen, K.: Nonlinear Multiobjective Optimization. Springer-Verlag, Berlin (1998)"},{"key":"956_CR23","unstructured":"Murtagh, B.A., Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H.: MINOS 5.51, Large Scale Nonlinear Solver (2004)"},{"issue":"1","key":"956_CR24","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1137\/18M1169680","volume":"29","author":"J Niebling","year":"2019","unstructured":"Niebling, J., Eichfelder, G.: A branch-and-bound-based algorithm for nonconvex multiobjective optimization. SIAM J. Optim. 29(1), 794\u2013821 (2019)","journal-title":"SIAM J. Optim."},{"key":"956_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-61007-8","volume-title":"Non-convex Multi-objective Optimizationn","author":"P Pardalos","year":"2017","unstructured":"Pardalos, P., \u017dilinskas, A., \u017dilinskas, J.: Non-convex Multi-objective Optimizationn. Springer-Verlag, Berlin (2017)"},{"key":"956_CR26","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/978-94-017-1247-7_7","volume-title":"Developments in Reliable Computing","author":"SM Rump","year":"1999","unstructured":"Rump, S.M.: INTLAB\u2014INTerval LABoratory. In: Csendes, T. (ed.) Developments in Reliable Computing, pp. 77\u2013104. Kluwer Academic Publishers, Dordrecht (1999)"},{"key":"956_CR27","volume-title":"Theory of Multiobjective Optimization","author":"Y Sawaragi","year":"1985","unstructured":"Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Cambridge (1985)"},{"key":"956_CR28","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1007\/s11750-009-0105-4","volume":"18","author":"D Scholz","year":"2010","unstructured":"Scholz, D.: The multicriteria big cube small cube method. TOP 18, 286\u2013302 (2010)","journal-title":"TOP"},{"key":"956_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-1951-8","volume-title":"Deterministic Global Optimization: Geometric Branch-and-Bound Methods and Their Applications","author":"D Scholz","year":"2012","unstructured":"Scholz, D.: Deterministic Global Optimization: Geometric Branch-and-Bound Methods and Their Applications. Springer, Berlin (2012)"},{"key":"956_CR30","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.cor.2016.07.012","volume":"78","author":"B Schulze","year":"2017","unstructured":"Schulze, B., Paquete, L., Klamroth, K., Figueira, J.R.: Bi-dimensional knapsack problems with one soft constraint. Comput. Oper. Res. 78, 15\u201326 (2017)","journal-title":"Comput. Oper. Res."},{"issue":"4","key":"956_CR31","doi-asserted-by":"publisher","first-page":"A2068","DOI":"10.1137\/15M1025773","volume":"38","author":"MS Darup","year":"2016","unstructured":"Darup, M.S., M\u00f6nnigmann, M.: Improved automatic computation of Hessian matrix spectral bounds. SIAM J. Sci. Comput. 38(4), A2068\u2013A2090 (2016)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"956_CR32","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s10479-015-2017-z","volume":"240","author":"C Segura","year":"2016","unstructured":"Segura, C., Coello, C.A.C., Miranda, G., Le\u00f3n, C.: Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization. Ann. Oper. Res. 240(1), 217\u2013250 (2016)","journal-title":"Ann. Oper. Res."},{"key":"956_CR33","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10107-005-0581-8","volume":"103","author":"M Tawarmalani","year":"2005","unstructured":"Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103, 225\u2013249 (2005)","journal-title":"Math. Program."},{"key":"956_CR34","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1007\/s10898-018-0622-5","volume":"74","author":"A \u017dilinskas","year":"2019","unstructured":"\u017dilinskas, A., Calvin, J.: Bi-objective decision making in global optimization based on statistical models. J. Global Optim. 74, 599\u2013609 (2019)","journal-title":"J. Global Optim."},{"issue":"1\u20133","key":"956_CR35","first-page":"89","volume":"21","author":"A \u017dilinskas","year":"2016","unstructured":"\u017dilinskas, A., \u017dilinskas, J.: Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems. Commun. Nonlinear Sci. Numer. Simul. 21(1\u20133), 89\u201398 (2016)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00956-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-020-00956-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00956-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T23:26:54Z","timestamp":1723764414000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-020-00956-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,15]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["956"],"URL":"https:\/\/doi.org\/10.1007\/s10898-020-00956-2","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2020,10,15]]},"assertion":[{"value":"5 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}