{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T11:06:42Z","timestamp":1769857602746,"version":"3.49.0"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T00:00:00Z","timestamp":1664409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s10957-022-02083-2","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T18:04:00Z","timestamp":1664474640000},"page":"418-448","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Properties, Extensions and Application of Piecewise Linearization for Euclidean Norm Optimization in $$\\mathbb {R}^2$$"],"prefix":"10.1007","volume":"195","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0796-1085","authenticated-orcid":false,"given":"Alo\u00efs","family":"Duguet","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9766-9864","authenticated-orcid":false,"given":"Christian","family":"Artigues","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5975-7639","authenticated-orcid":false,"given":"Laurent","family":"Houssin","sequence":"additional","affiliation":[]},{"given":"Sandra Ulrich","family":"Ngueveu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"issue":"10","key":"2083_CR1","doi-asserted-by":"publisher","first-page":"1274","DOI":"10.1287\/mnsc.32.10.1274","volume":"32","author":"WP Adams","year":"1986","unstructured":"Adams, W.P., Sherali, H.D.: A tight linearization and an algorithm for zero-one quadratic programming problems. Manage. Sci. 32(10), 1274\u20131290 (1986). https:\/\/doi.org\/10.1287\/mnsc.32.10.1274","journal-title":"Manage. Sci."},{"issue":"3","key":"2083_CR2","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1109\/TPWRS.2008.926704","volume":"23","author":"A Borghetti","year":"2008","unstructured":"Borghetti, A., D\u2019Ambrosio, C., Lodi, A., Martello, S.: An MILP approach for short-term hydro scheduling and unit commitment with head-dependent reservoir. IEEE Trans. Power Syst. 23(3), 1115\u20131124 (2008). https:\/\/doi.org\/10.1109\/TPWRS.2008.926704","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"2083_CR3","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1080\/10556788.2018.1556661","volume":"35","author":"R Burlacu","year":"2020","unstructured":"Burlacu, R., Gei\u00dfler, B., Schewe, L.: Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes. Optim. Methods Softw. 35(1), 37\u201364 (2020). https:\/\/doi.org\/10.1080\/10556788.2018.1556661","journal-title":"Optim. Methods Softw."},{"key":"2083_CR4","doi-asserted-by":"publisher","unstructured":"Camino, J.-T., Mourgues, S.,\u00a0Artigues, C.,\u00a0Houssin, L.: A greedy approach combined with graph coloring for non-uniform beam layouts under antenna constraints in multibeam satellite systems. In: 2014 7th Advanced Satellite Multimedia Systems Conference and the 13th Signal Processing for Space Communications Workshop (ASMS\/SPSC), pp. 374\u2013381. https:\/\/doi.org\/10.1109\/ASMS-SPSC.2014.6934570","DOI":"10.1109\/ASMS-SPSC.2014.6934570"},{"key":"2083_CR5","doi-asserted-by":"publisher","unstructured":"Camino, J.-T., Artigues, C.,\u00a0Houssin, L.,\u00a0Mourgues, S.: Mixed-integer linear programming for multibeam satellite systems design: Application to the beam layout optimization. In: 2016 Annual IEEE Systems Conference (SysCon), pp. 1\u20136. https:\/\/doi.org\/10.1109\/SYSCON.2016.7490613","DOI":"10.1109\/SYSCON.2016.7490613"},{"key":"2083_CR6","doi-asserted-by":"publisher","unstructured":"Camino, J.-T.,\u00a0Artigues, C., Houssin, L.,\u00a0Mourgues, S.: Linearisation of euclidean norm dependent inequalities applied to multibeam satellites design. Comput. Optim. Appl. (2019). https:\/\/doi.org\/10.1007\/s10589-019-00083-z","DOI":"10.1007\/s10589-019-00083-z"},{"key":"2083_CR7","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s11081-009-9093-3","volume":"12","author":"E Camponogara","year":"2011","unstructured":"Camponogara, E., de Castro, M.P., Plucenio, A., Pagano, D.J.: Compressor scheduling in oil fields. Optim. Eng. 12, 153\u2013174 (2011). https:\/\/doi.org\/10.1007\/s11081-009-9093-3","journal-title":"Optim. Eng."},{"issue":"3","key":"2083_CR8","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1109\/99.714603","volume":"5","author":"J Czyzyk","year":"1998","unstructured":"Czyzyk, J., Mesnier, M.P., Mor\u00e9, J.J.: The neos server. IEEE J. Comput. Sci. Eng. 5(3), 68\u201375 (1998)","journal-title":"IEEE J. Comput. Sci. Eng."},{"issue":"1","key":"2083_CR9","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.orl.2009.09.005","volume":"38","author":"C D\u2019Ambrosio","year":"2010","unstructured":"D\u2019Ambrosio, C., Lodi, A., Martello, S.: Piecewise linear approximation of functions of two variables in MILP models. Oper. Res. Lett. 38(1), 39\u201346 (2010). https:\/\/doi.org\/10.1016\/j.orl.2009.09.005","journal-title":"Oper. Res. Lett."},{"key":"2083_CR10","doi-asserted-by":"crossref","unstructured":"Dolan, E.D.: The neos server 4.0 administrative guide. Technical Memorandum ANL\/MCS-TM-250, Mathematics and Computer Science Division, Argonne National Laboratory (2001)","DOI":"10.2172\/822567"},{"issue":"1","key":"2083_CR11","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/TPAMI.1986.4767753","volume":"8","author":"JG Dunham","year":"1986","unstructured":"Dunham, J.G.: Optimum uniform piecewise linear approximation of planar curves. IEEE Trans. Pattern Anal. Mach. Intell. PAMI 8(1), 67\u201375 (1986). https:\/\/doi.org\/10.1109\/TPAMI.1986.4767753","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell. PAMI"},{"key":"2083_CR12","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/978-1-4614-1927-3_10","volume-title":"Mixed Integer Nonlinear Programming","author":"B Gei\u00dfler","year":"2012","unstructured":"Gei\u00dfler, B., Martin, A., Morsi, A., Schewe, L.: Using piecewise linear functions for solving MINLPs. In: Lee, J., Leyffer, S. (eds.) Mixed Integer Nonlinear Programming, pp. 287\u2013314. Springer, New York (2012)"},{"key":"2083_CR13","first-page":"167","volume-title":"Approximation Theory and Optimization","author":"W Gropp","year":"1997","unstructured":"Gropp, W., Mor\u00e9, J.J.: Optimization environments and the neos server. In: Buhman, M.D., Iserles, A. (eds.) Approximation Theory and Optimization, pp. 167\u2013182. Cambridge University Press, Cambridge (1997)"},{"issue":"1","key":"2083_CR14","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0012-365X(95)00075-8","volume":"158","author":"RB Hughes","year":"1996","unstructured":"Hughes, R.B., Anderson, M.R.: Simplexity of the cube. Discret. Math. 158(1), 99\u2013150 (1996). https:\/\/doi.org\/10.1016\/0012-365X(95)00075-8","journal-title":"Discret. Math."},{"key":"2083_CR15","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s10898-013-0125-3","volume":"59","author":"J Kallrath","year":"2014","unstructured":"Kallrath, J., Rebennack, S.: Cutting ellipses from area-minimizing rectangles. J. Global Optim. 59, 405\u2013437 (2014). https:\/\/doi.org\/10.1007\/s10898-013-0125-3","journal-title":"J. Global Optim."},{"issue":"1","key":"2083_CR16","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/S0167-6377(03)00059-2","volume":"32","author":"AB Keha","year":"2004","unstructured":"Keha, A.B., de Farias, I.R., Nemhauser, G.L.: Models for representing piecewise linear cost functions. Oper. Res. Lett. 32(1), 44\u201348 (2004). https:\/\/doi.org\/10.1016\/S0167-6377(03)00059-2","journal-title":"Oper. Res. Lett."},{"key":"2083_CR17","doi-asserted-by":"publisher","unstructured":"Liberti, L.,\u00a0Cafieri, S.,\u00a0Tarissan, F.: Reformulations in mathematical programming: a computational approach. In: Abraham, A., Hassanien, A.-E.,\u00a0Siarry, P.,\u00a0Engelbrecht, A. (eds.) Foundations of Computational Intelligence Volume 3: Global Optimization, pp. 153\u2013234. Springer, Berlin, Heidelberg (2009). ISBN 978-3-642-01085-9. https:\/\/doi.org\/10.1007\/978-3-642-01085-9_7","DOI":"10.1007\/978-3-642-01085-9_7"},{"key":"2083_CR18","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s11590-008-0095-4","volume":"3","author":"L Liberti","year":"2009","unstructured":"Liberti, L., Maculan, N., Zhang, Y.: Optimal configuration of gamma ray machine radiosurgery units: The sphere covering subproblem. Optim. Lett. 3, 109\u2013121 (2009). https:\/\/doi.org\/10.1007\/s11590-008-0095-4","journal-title":"Optim. Lett."},{"key":"2083_CR19","doi-asserted-by":"crossref","unstructured":"Liberti, L.S.: Reformulation and Convex Relaxation Techniques for Global Optimization. PhD thesis, Imperial College London (2004)","DOI":"10.1007\/s10288-004-0038-6"},{"issue":"13","key":"2083_CR20","doi-asserted-by":"publisher","first-page":"6098","DOI":"10.1021\/ie8012117","volume":"48","author":"R Misener","year":"2009","unstructured":"Misener, R., Gounaris, C.E., Floudas, C.A.: Global optimization of gas lifting operations: a comparative study of piecewise linear formulations. Ind. Eng. Chem. Res. 48(13), 6098\u20136104 (2009). https:\/\/doi.org\/10.1021\/ie8012117","journal-title":"Ind. Eng. Chem. Res."},{"key":"2083_CR21","unstructured":"Muts, P.: Decomposition methods for mixed-integer nonlinear programming. PhD thesis (2021)"},{"key":"2083_CR22","doi-asserted-by":"publisher","unstructured":"Muts, P.,\u00a0Nowak, I.: Towards multi-tree methods for large-scale global optimization. In: Le Thi, H.A., Le, H.M.,\u00a0PhamDinh, T. (eds.) Optimization of Complex Systems: Theory, Models, Algorithms and Applications, pp. 498\u2013506. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-21803-4_50","DOI":"10.1007\/978-3-030-21803-4_50"},{"issue":"3","key":"2083_CR23","doi-asserted-by":"publisher","first-page":"1058","DOI":"10.1016\/j.ejor.2018.11.021","volume":"275","author":"SU Ngueveu","year":"2019","unstructured":"Ngueveu, S.U.: Piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming-based solution methods. Eur. J. Oper. Res. 275(3), 1058\u20131071 (2019). https:\/\/doi.org\/10.1016\/j.ejor.2018.11.021","journal-title":"Eur. J. Oper. Res."},{"key":"2083_CR24","doi-asserted-by":"publisher","unstructured":"Nowak, I.: Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming. Birkh\u00e4user (2005). https:\/\/doi.org\/10.1007\/3-7643-7374-1","DOI":"10.1007\/3-7643-7374-1"},{"issue":"1","key":"2083_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0167-6377(00)00028-6","volume":"27","author":"M Padberg","year":"2000","unstructured":"Padberg, M.: Approximating separable nonlinear functions via mixed zero-one programs. Oper. Res. Lett. 27(1), 1\u20135 (2000). https:\/\/doi.org\/10.1016\/S0167-6377(00)00028-6","journal-title":"Oper. Res. Lett."},{"issue":"3","key":"2083_CR26","doi-asserted-by":"publisher","first-page":"1054","DOI":"10.2514\/6.2007-3179","volume":"21","author":"S Rao","year":"2006","unstructured":"Rao, S., Tang, M., Hsu, C.-C.: Multiple beam antenna technology for satellite communications payloads. ACES J. 21(3), 1054\u20134887 (2006). https:\/\/doi.org\/10.2514\/6.2007-3179","journal-title":"ACES J."},{"key":"2083_CR27","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1007\/s10957-014-0688-2","volume":"167","author":"S Rebennack","year":"2015","unstructured":"Rebennack, S., Kallrath, J.: Continuous piecewise linear delta-approximations for bivariate and multivariate functions. J. Optim. Theory Appl. 167, 102\u2013117 (2015). https:\/\/doi.org\/10.1007\/s10957-014-0688-2","journal-title":"J. Optim. Theory Appl."},{"key":"2083_CR28","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/s10957-014-0687-3","volume":"167","author":"S Rebennack","year":"2015","unstructured":"Rebennack, S., Kallrath, J.: Continuous piecewise linear delta-approximations for univariate functions: computing minimal breakpoint systems. J. Optim. Theory Appl. 167, 617\u2013643 (2015). https:\/\/doi.org\/10.1007\/s10957-014-0687-3","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"2083_CR29","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1287\/ijoc.2019.0890","volume":"32","author":"S Rebennack","year":"2020","unstructured":"Rebennack, S., Krasko, V.: Piecewise linear function fitting via mixed-integer linear programming. Inform. J. Comput. 32(2), 507\u2013530 (2020). https:\/\/doi.org\/10.1287\/ijoc.2019.0890","journal-title":"Inform. J. Comput."},{"key":"2083_CR30","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/BF01580581","volume":"34","author":"J Rosen","year":"1986","unstructured":"Rosen, J., Pardalos, P.: Global minimization of large-scale constrained concave quadratic problems by separable programming. Math. Program. 34, 163\u2013174 (1986). https:\/\/doi.org\/10.1007\/BF01580581","journal-title":"Math. Program."},{"issue":"3","key":"2083_CR31","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.ejor.2014.03.020","volume":"239","author":"R Rovatti","year":"2014","unstructured":"Rovatti, R., D\u2019Ambrosio, C., Lodi, A., Martello, S.: Optimistic MILP modeling of non-linear optimization problems. Eur. J. Oper. Res. 239(3), 32\u201345 (2014). https:\/\/doi.org\/10.1016\/j.ejor.2014.03.020","journal-title":"Eur. J. Oper. Res."},{"key":"2083_CR32","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.jnca.2018.04.007","volume":"114","author":"A Santoyo-Gonz\u00e1lez","year":"2018","unstructured":"Santoyo-Gonz\u00e1lez, A., Cervell\u00f3-Pastor, C.: Latency-aware cost optimization of the service infrastructure placement in 5g networks. J. Netw. Comput. Appl. 114, 29\u201337 (2018). https:\/\/doi.org\/10.1016\/j.jnca.2018.04.007","journal-title":"J. Netw. Comput. Appl."},{"key":"2083_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4388-3","volume-title":"A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems","author":"HD Sherali","year":"1999","unstructured":"Sherali, H.D., Adams, W.P.: A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer Academic Publishers, Dodrecht (1999)"},{"key":"2083_CR34","doi-asserted-by":"publisher","unstructured":"Sherali, H.D.,\u00a0Liberti, L.: Reformulation-linearization technique for global optimization. In: Floudas, C.A., Pardalos, P.M. (eds.) Encyclopedia of Optimization, pp. 3263\u20133268. Springer, Boston (2009). ISBN 978-0-387-74759-0. https:\/\/doi.org\/10.1007\/978-0-387-74759-0_559","DOI":"10.1007\/978-0-387-74759-0_559"},{"issue":"3","key":"2083_CR35","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1016\/j.ejor.2013.07.040","volume":"232","author":"TL Silva","year":"2014","unstructured":"Silva, T.L., Camponogara, E.: A computational analysis of multidimensional piecewise-linear models with applications to oil production optimization. Eur. J. Oper. Res. 232(3), 630\u2013642 (2014). https:\/\/doi.org\/10.1016\/j.ejor.2013.07.040","journal-title":"Eur. J. Oper. Res."},{"issue":"4","key":"2083_CR36","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/S0098-1354(98)00286-5","volume":"23","author":"E Smith","year":"1999","unstructured":"Smith, E., Pantelides, C.: A symbolic reformulation\/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Comput. Chem. Eng. 23(4), 457\u2013478 (1999). https:\/\/doi.org\/10.1016\/S0098-1354(98)00286-5","journal-title":"Comput. Chem. Eng."},{"issue":"1","key":"2083_CR37","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1006\/eujc.1999.0327","volume":"21","author":"WD Smith","year":"2000","unstructured":"Smith, W.D.: A lower bound for the simplexity of then-cube via hyperbolic volumes. Eur. J. Comb. 21(1), 131\u2013137 (2000). https:\/\/doi.org\/10.1006\/eujc.1999.0327","journal-title":"Eur. J. Comb."},{"issue":"6","key":"2083_CR38","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.orl.2013.08.010","volume":"41","author":"S Sridhar","year":"2013","unstructured":"Sridhar, S., Linderoth, J., Luedtke, J.: Locally ideal formulations for piecewise linear functions with indicator variables. Oper. Res. Lett. 41(6), 627\u2013632 (2013). https:\/\/doi.org\/10.1016\/j.orl.2013.08.010","journal-title":"Oper. Res. Lett."},{"key":"2083_CR39","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s11590-007-0065-2","volume":"2","author":"F Tardella","year":"2007","unstructured":"Tardella, F.: Existence and sum decomposition of vertex polyhedral convex envelopes. Optim. Lett. 2, 363\u2013375 (2007). https:\/\/doi.org\/10.1007\/s11590-007-0065-2","journal-title":"Optim. Lett."},{"key":"2083_CR40","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s10107-009-0295-4","volume":"128","author":"JP Vielma","year":"2011","unstructured":"Vielma, J.P., Nemhauser, G.L.: Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Math. Program. Ser. A 128, 49\u201372 (2011). https:\/\/doi.org\/10.1007\/s10107-009-0295-4","journal-title":"Math. Program. Ser. A"},{"issue":"1","key":"2083_CR41","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.cam.2007.02.006","volume":"214","author":"H Zhang","year":"2008","unstructured":"Zhang, H., Wang, S.: Linearly constrained global optimization via piecewise-linear approximation. J. Comput. Appl. Math. 214(1), 111\u2013120 (2008). https:\/\/doi.org\/10.1016\/j.cam.2007.02.006","journal-title":"J. Comput. Appl. Math."},{"key":"2083_CR42","doi-asserted-by":"publisher","unstructured":"Zhou, C., Mazumder, A.,\u00a0Das, A.,\u00a0Basu, K.,\u00a0Matin-Moghaddam, N.,\u00a0Mehrani, S.,\u00a0Sen, A.: Relay node placement under budget constraint. In: Proceedings of the 19th International Conference on Distributed Computing and Networking, pp. 1\u201311 (2018). https:\/\/doi.org\/10.1145\/3154273.3154302","DOI":"10.1145\/3154273.3154302"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02083-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02083-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02083-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T21:10:55Z","timestamp":1667596255000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02083-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,29]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["2083"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02083-2","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,29]]},"assertion":[{"value":"21 July 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}