{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T14:45:49Z","timestamp":1751467549906,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T00:00:00Z","timestamp":1669680000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T00:00:00Z","timestamp":1669680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1007\/s10898-022-01254-9","type":"journal-article","created":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T09:04:22Z","timestamp":1669712662000},"page":"37-60","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Nonconvex sensitivity-based generalized Benders decomposition"],"prefix":"10.1007","volume":"86","author":[{"given":"Jia-Jiang","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3677-3182","authenticated-orcid":false,"given":"Xiong-Lin","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,29]]},"reference":[{"key":"1254_CR1","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1016\/0098-1354(91)85027-R","volume":"15","author":"NV Sahinidis","year":"1991","unstructured":"Sahinidis, N.V., Grossmann, I.E.: Convergence properties of generalized Benders decomposition. Comput. Chem. Eng. 15, 481\u2013491 (1991)","journal-title":"Comput. Chem. Eng."},{"key":"1254_CR2","doi-asserted-by":"publisher","first-page":"2379","DOI":"10.1002\/aic.14022","volume":"59","author":"Y Chu","year":"2013","unstructured":"Chu, Y., You, F.: Integrated scheduling and dynamic optimization of sequential batch processes with online implementation. AIChE J. 59, 2379\u20132406 (2013)","journal-title":"AIChE J."},{"key":"1254_CR3","doi-asserted-by":"publisher","first-page":"16851","DOI":"10.1021\/ie402621t","volume":"52","author":"Y Chu","year":"2013","unstructured":"Chu, Y., You, F.: Integration of scheduling and dynamic optimization of batch processes under uncertainty: two-stage stochastic programming approach and enhanced generalized benders decomposition algorithm. Ind. Eng. Chem. Res. 52, 16851\u201316869 (2013)","journal-title":"Ind. Eng. Chem. Res."},{"key":"1254_CR4","doi-asserted-by":"publisher","first-page":"7867","DOI":"10.1021\/ie400475s","volume":"52","author":"Y Chu","year":"2013","unstructured":"Chu, Y., You, F.: Integrated scheduling and dynamic optimization of complex batch processes with general network structure using a generalized benders decomposition approach. Ind. Eng. Chem. Res. 52, 7867\u20137885 (2013)","journal-title":"Ind. Eng. Chem. Res."},{"key":"1254_CR5","doi-asserted-by":"publisher","first-page":"3416","DOI":"10.1002\/aic.13738","volume":"58","author":"Y Nie","year":"2012","unstructured":"Nie, Y., Biegler, L.T., Wassick, J.M.: Integrated scheduling and dynamic optimization of batch processes using state equipment networks. AIChE J. 58, 3416\u20133432 (2012)","journal-title":"AIChE J."},{"key":"1254_CR6","doi-asserted-by":"publisher","first-page":"4303","DOI":"10.1021\/ie502960p","volume":"54","author":"Y Nie","year":"2015","unstructured":"Nie, Y., Biegler, L.T., Villa, C.M., Wassick, J.M.: Discrete time formulation for the integration of scheduling and dynamic optimization. Ind. Eng. Chem. Res. 54, 4303\u20134315 (2015)","journal-title":"Ind. Eng. Chem. Res."},{"key":"1254_CR7","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/j.ces.2011.09.024","volume":"68","author":"C Liu","year":"2012","unstructured":"Liu, C., Zhao, C., Xu, Q.: Integration of electroplating process design and operation for simultaneous productivity maximization, energy saving, and freshwater minimization. Chem. Eng. Sci. 68, 202\u2013214 (2012)","journal-title":"Chem. Eng. Sci."},{"key":"1254_CR8","doi-asserted-by":"publisher","first-page":"7287","DOI":"10.1021\/ie201262f","volume":"51","author":"X Li","year":"2012","unstructured":"Li, X., Chen, Y., Barton, P.I.: Nonconvex generalized benders decomposition with piecewise convex relaxations for global optimization of integrated process design and operation problems. Ind. Eng. Chem. Res. 51, 7287\u20137299 (2012)","journal-title":"Ind. Eng. Chem. Res."},{"key":"1254_CR9","doi-asserted-by":"crossref","unstructured":"Sarabia, D., de Prada, C., Cristea, S.: Hybrid predictive control of a simulated continuous-batch process. In:\u00a0\u00a0Proceedings\u00a0of the\u00a0International Conference\u00a0on\u00a0Control Applications, pp.\u00a01400\u20131407 (2007)","DOI":"10.1109\/CCA.2007.4389432"},{"key":"1254_CR10","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1016\/B978-0-444-64241-7.50107-5","volume":"44","author":"C De Prada","year":"2018","unstructured":"De Prada, C., Mazaeda, R., Podar, S.: Optimal operation of a combined continuous\u2013batch process. Comput. Aid. Chem. Eng. 44, 673\u2013678 (2018)","journal-title":"Comput. Aid. Chem. Eng."},{"key":"1254_CR11","doi-asserted-by":"publisher","first-page":"1511","DOI":"10.1002\/aic.13924","volume":"59","author":"D Yue","year":"2013","unstructured":"Yue, D., You, F.: Planning and scheduling of flexible process networks under uncertainty with stochastic inventory: MINLP models and algorithm. AIChE J. 59, 1511\u20131532 (2013)","journal-title":"AIChE J."},{"key":"1254_CR12","doi-asserted-by":"publisher","first-page":"3160","DOI":"10.1002\/aic.11658","volume":"54","author":"S Terrazas-Moreno","year":"2008","unstructured":"Terrazas-Moreno, S., Flores-Tlacuahuac, A., Grossmann, I.E.: Simultaneous design, scheduling, and optimal control of a methyl-methacrylate continuous polymerization reactor. AIChE J. 54, 3160\u20133170 (2008)","journal-title":"AIChE J."},{"key":"1254_CR13","doi-asserted-by":"publisher","first-page":"100902","DOI":"10.1016\/j.nahs.2020.100902","volume":"37","author":"J Lin","year":"2020","unstructured":"Lin, J., Luo, X.: Hybrid parametric minimum principle. Nonlinear Anal. -Hybri. 37, 100902 (2020). https:\/\/doi.org\/10.1016\/j.nahs.2020.100902","journal-title":"Nonlinear Anal. -Hybri"},{"key":"1254_CR14","doi-asserted-by":"publisher","first-page":"23187","DOI":"10.1021\/acs.iecr.9b03416","volume":"58","author":"J Lin","year":"2019","unstructured":"Lin, J., Xu, F., Luo, X.: Dynamic optimization of continuous-batch processes: a case study of an FCCU with CO promoter. Ind. Eng. Chem. Res. 58, 23187\u201323200 (2019)","journal-title":"Ind. Eng. Chem. Res."},{"key":"1254_CR15","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/BF00934810","volume":"10","author":"AM Geoffrion","year":"1972","unstructured":"Geoffrion, A.M.: Generalized benders decomposition. J. Optim.Theory App. 10, 237\u2013260 (1972)","journal-title":"J. Optim.Theory App."},{"key":"1254_CR16","first-page":"1","volume":"31","author":"Z Li","year":"2015","unstructured":"Li, Z., Wu, W., Zhang, B., Wang, B.: Decentralized multi-area dynamic economic dispatch using modified generalized benders decomposition. IEEE T. Power Syst. 31, 1\u201313 (2015)","journal-title":"IEEE T. Power Syst."},{"key":"1254_CR17","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1137\/080742026","volume":"21","author":"M Chen","year":"2011","unstructured":"Chen, M., Mehrotra, S.: Self-concordance and decomposition-based interior point methods for the two-stage stochastic convex optimization problem. SIAM J. Optim. 21, 1667\u20131687 (2011)","journal-title":"SIAM J. Optim."},{"key":"1254_CR18","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1137\/17M1128204","volume":"28","author":"R Rahmaniani","year":"2018","unstructured":"Rahmaniani, R., Crainic, T.G., Gendreau, M., Rei, W.: Accelerating the benders decomposition method: application to stochastic network design problems. SIAM J. Optim. 28, 875\u2013903 (2018)","journal-title":"SIAM J. Optim."},{"key":"1254_CR19","doi-asserted-by":"publisher","first-page":"2474","DOI":"10.1137\/080741380","volume":"20","author":"S Mehrotra","year":"2010","unstructured":"Mehrotra, S., G\u00f6khan-\u00d6zevin, M.: Convergence of a weighted barrier decomposition algorithm for two-stage stochastic programming with discrete support. SIAM J. Optim. 20, 2474\u20132486 (2010)","journal-title":"SIAM J. Optim."},{"key":"1254_CR20","doi-asserted-by":"publisher","first-page":"1466","DOI":"10.1021\/ie00006a008","volume":"31","author":"DK Varvarezos","year":"1992","unstructured":"Varvarezos, D.K., Grossmann, I.E., Biegler, L.T.: An outer-approximation method for multiperiod design optimization. Ind. Eng. Chem. Res. 31, 1466\u20131477 (1992)","journal-title":"Ind. Eng. Chem. Res."},{"key":"1254_CR21","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/BF02592064","volume":"36","author":"MA Duran","year":"1986","unstructured":"Duran, M.A., Grossmann, I.E.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Program. 36, 307\u2013339 (1986)","journal-title":"Math. Program."},{"key":"1254_CR22","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1007\/s10957-015-0715-y","volume":"167","author":"Z Wei","year":"2015","unstructured":"Wei, Z., Ali, M.M.: Outer approximation algorithm for one class of convex mixed-integer nonlinear programming problems with partial differentiability. J. Optim. Theory App. 167, 644\u2013652 (2015)","journal-title":"J. Optim. Theory App."},{"key":"1254_CR23","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1016\/0098-1354(90)87085-4","volume":"14","author":"J Viswanathan","year":"1990","unstructured":"Viswanathan, J., Grossmann, I.E.: A combined penalty function and outer-approximation method for MINLP optimization. Comput. Chem. Eng. 14, 769\u2013782 (1990)","journal-title":"Comput. Chem. Eng."},{"key":"1254_CR24","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/BF01581153","volume":"66","author":"R Fletcher","year":"1994","unstructured":"Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66, 327\u2013349 (1994)","journal-title":"Math. Program."},{"key":"1254_CR25","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s10957-011-9888-1","volume":"151","author":"X Li","year":"2011","unstructured":"Li, X., Tomasgard, A., Barton, P.I.: Nonconvex generalized benders decomposition for stochastic separable mixed-integer nonlinear programs. J. Optim. Theory App. 151, 425\u2013454 (2011)","journal-title":"J. Optim. Theory App."},{"issue":"2","key":"1254_CR26","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s10898-019-00816-8","volume":"75","author":"C Li","year":"2019","unstructured":"Li, C., Grossmann, I.E.: A generalized benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary rst and second stage variables. J. Global Optim. 75(2), 247\u2013272 (2019)","journal-title":"J. Global Optim."},{"issue":"3","key":"1254_CR27","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s10898-019-00786-x","volume":"75","author":"E Ogbe","year":"2019","unstructured":"Ogbe, E., Li, X.: A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs. J. Global Optim. 75(3), 595\u2013629 (2019)","journal-title":"J. Global Optim."},{"key":"1254_CR28","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1016\/S0098-1354(02)00261-2","volume":"27","author":"V Bansal","year":"2003","unstructured":"Bansal, V., Sakizlis, V., Ross, R., Perkins, J.D., Pistikopoulos, E.N.: New algorithms for mixed-integer dynamic optimization. Comput. Chem. Eng. 27, 647\u2013668 (2003)","journal-title":"Comput. Chem. Eng."},{"key":"1254_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0165-1765(00)00227-5","volume":"68","author":"ML Weitzman","year":"2000","unstructured":"Weitzman, M.L.: An \u2018economics proof\u2019 of the supporting hyperplane theorem. Econ. Lett. 68, 1\u20136 (2000)","journal-title":"Econ. Lett."},{"key":"1254_CR30","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1090\/S0273-0979-1983-15185-6","volume":"9","author":"SS Antman","year":"1983","unstructured":"Antman, S.S.: The influence of elasticity on analysis: modern developments. B Am. Math. Soc. 9, 267\u2013292 (1983)","journal-title":"B Am. Math. Soc."},{"key":"1254_CR31","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/S0377-0427(00)00367-8","volume":"122","author":"RA Lorentz","year":"2000","unstructured":"Lorentz, R.A.: Multivariate hermite interpolation by algebraic polynomials: a survey. J. Comput. Appl. Math. 122, 167\u2013201 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"1254_CR32","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.compchemeng.2013.04.006","volume":"55","author":"X Li","year":"2013","unstructured":"Li, X.: Parallel nonconvex generalized Benders decomposition for natural gas production network planning under uncertainty. Comput. Chem. Eng. 55, 97\u2013108 (2013)","journal-title":"Comput. Chem. Eng."},{"key":"1254_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2021.12.001","volume":"147","author":"N Liu","year":"2022","unstructured":"Liu, N., Wang, J., Qin, S.: A one-layer recurrent neural network for nonsmooth pseudoconvex optimization with quasiconvex inequality and affine equality constraints. Neural Netw. 147, 1\u20139 (2022)","journal-title":"Neural Netw."},{"issue":"4","key":"1254_CR34","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1137\/0108053","volume":"8","author":"JE Kelley","year":"1960","unstructured":"Kelley, J.E.: The cutting-plane method for solving convex programs. J. Soc. Ind. Appl. Math. 8(4), 703\u2013712 (1960)","journal-title":"J. Soc. Ind. Appl. Math."},{"issue":"1","key":"1254_CR35","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1021\/ie401777n","volume":"53","author":"R Wang","year":"2014","unstructured":"Wang, R., Luo, X., Xu, F.: Economic and control performance of a Fluid Catalytic cracking unit: interactions between combustion air and CO promoters. Ind. Eng. Chem. Res. 53(1), 287\u2013304 (2014)","journal-title":"Ind. Eng. Chem. Res."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-022-01254-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-022-01254-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-022-01254-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T11:06:04Z","timestamp":1681988764000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-022-01254-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,29]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["1254"],"URL":"https:\/\/doi.org\/10.1007\/s10898-022-01254-9","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2022,11,29]]},"assertion":[{"value":"7 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 November 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 November 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}