{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T10:01:25Z","timestamp":1648807285777},"reference-count":94,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,3,8]],"date-time":"2015-03-08T00:00:00Z","timestamp":1425772800000},"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":["Oper Res Int J"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1007\/s12351-015-0171-3","type":"journal-article","created":{"date-parts":[[2015,3,7]],"date-time":"2015-03-07T09:01:41Z","timestamp":1425718901000},"page":"163-198","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A generic column generation principle: derivation and convergence analysis"],"prefix":"10.1007","volume":"15","author":[{"given":"Torbj\u00f6rn","family":"Larsson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Athanasios","family":"Migdalas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Patriksson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,3,8]]},"reference":[{"key":"171_CR1","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1287\/trsc.3.1.53","volume":"3","author":"LH Appelgren","year":"1969","unstructured":"Appelgren LH (1969) A column generation algorithm for a ship scheduling problem. Transp Sci 3:53\u201368","journal-title":"Transp Sci"},{"key":"171_CR2","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1287\/trsc.5.1.64","volume":"5","author":"LH Appelgren","year":"1971","unstructured":"Appelgren LH (1971) Integer programming methods for a vessel scheduling problem. Transp Sci 5:64\u201378","journal-title":"Transp Sci"},{"key":"171_CR3","volume-title":"Set-valued analysis","author":"J-P Aubin","year":"1990","unstructured":"Aubin J-P, Frankowska H (1990) Set-valued analysis. Birkh\u00e4user, Boston"},{"key":"171_CR4","volume-title":"Optimisation: M\u00e9thodes Num\u00e9riques","author":"A Auslender","year":"1976","unstructured":"Auslender A (1976) Optimisation: M\u00e9thodes Num\u00e9riques. Masson, Paris"},{"key":"171_CR5","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1287\/trsc.36.4.398.549","volume":"36","author":"H Bar-Gera","year":"2002","unstructured":"Bar-Gera H (2002) Origin-based algorithm for the traffic assignment problem. Transp Sci 36:398\u2013417","journal-title":"Transp Sci"},{"key":"171_CR6","first-page":"1022","volume":"44","author":"H Bar-Gera","year":"2010","unstructured":"Bar-Gera H (2010) Traffic assignment by paired alternative segments. Transp Sci 44:1022\u20131046","journal-title":"Transp Sci"},{"key":"171_CR7","doi-asserted-by":"crossref","DOI":"10.1002\/0471787779","volume-title":"Nonlinear programming: theory and algorithms","author":"MS Bazaraa","year":"2006","unstructured":"Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming: theory and algorithms, 3rd edn. Wiley, New York","edition":"3"},{"key":"171_CR8","volume-title":"Nonlinear programming","author":"DP Bertsekas","year":"1999","unstructured":"Bertsekas DP (1999) Nonlinear programming. Athena Scientific, Belmont"},{"key":"171_CR9","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1137\/090772204","volume":"21","author":"DP Bertsekas","year":"2011","unstructured":"Bertsekas DP, Yu H (2011) A unifying polyhedral approximation framework for convex optimization. SIAM J Optim 21:333\u2013360","journal-title":"SIAM J Optim"},{"key":"171_CR10","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1061\/(ASCE)0733-947X(2004)130:1(49)","volume":"130","author":"D Boyce","year":"2004","unstructured":"Boyce D, Ralevic-Dekic B, Bar-Gera H (2004) Convergence of traffic assignments: How much is enough? J Transp Eng 130:49\u201355","journal-title":"J Transp Eng"},{"key":"171_CR11","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1137\/0725068","volume":"25","author":"JV Burke","year":"1988","unstructured":"Burke JV, Mor\u00e9 JJ (1988) On the identification of active constraints. SIAM J Numer Anal 25:1197\u20131211","journal-title":"SIAM J Numer Anal"},{"key":"171_CR12","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1137\/0804032","volume":"3","author":"JV Burke","year":"1994","unstructured":"Burke JV, Mor\u00e9 JJ (1994) Exposing constraints. SIAM J Optim 3:573\u2013595","journal-title":"SIAM J Optim"},{"key":"171_CR13","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1137\/0306032","volume":"6","author":"MD Canon","year":"1968","unstructured":"Canon MD, Cullum CD (1968) A tight upper bound on the rate of convergence of the Frank\u2013Wolfe algorithm. SIAM J Control 6:509\u2013516","journal-title":"SIAM J Control"},{"key":"171_CR14","doi-asserted-by":"crossref","first-page":"2724","DOI":"10.1016\/j.cor.2013.05.012","volume":"40","author":"E \u00c7elebi","year":"2013","unstructured":"\u00c7elebi E, Fuller JD (2013) Master problem approximations in Dantzig\u2013Wolfe decomposition of variational inequality problems with applications to two energy market models. Comput Oper Res 40:2724\u20132739","journal-title":"Comput Oper Res"},{"key":"171_CR15","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF00934554","volume":"32","author":"G Cohen","year":"1980","unstructured":"Cohen G (1980) Auxiliary problem principle and decomposition of optimization problems. J Optim Theory Appl 32:277\u2013305","journal-title":"J Optim Theory Appl"},{"key":"171_CR16","series-title":"Vol. 1 of MPS-SIAM series on optimization","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-region methods","author":"AR Conn","year":"2000","unstructured":"Conn AR, Gould NIM, Toint PhL (2000) Trust-region methods., Vol. 1 of MPS-SIAM series on optimization, SIAM, Philadelphia"},{"key":"171_CR17","volume-title":"The theory of max\u2013min","author":"JM Danskin","year":"1967","unstructured":"Danskin JM (1967) The theory of max\u2013min. Springer, Berlin"},{"key":"171_CR18","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1287\/opre.8.1.101","volume":"8","author":"GB Dantzig","year":"1960","unstructured":"Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8:101\u2013111","journal-title":"Oper Res"},{"key":"171_CR19","doi-asserted-by":"crossref","first-page":"767","DOI":"10.2307\/1911818","volume":"29","author":"GB Dantzig","year":"1961","unstructured":"Dantzig GB, Wolfe P (1961) The decomposition algorithm for linear programs. Econometrica 29:767\u2013778","journal-title":"Econometrica"},{"key":"171_CR20","volume-title":"Introduction to minimax","author":"VF Dem\u2019yanov","year":"1974","unstructured":"Dem\u2019yanov VF, Malozemov VN (1974) Introduction to minimax. Wiley, New York"},{"key":"171_CR21","volume-title":"Systems analysis by multilevel methods","author":"YMI Dirickx","year":"1979","unstructured":"Dirickx YMI, Jennergren LP (1979) Systems analysis by multilevel methods. Wiley, Chichester"},{"key":"171_CR22","doi-asserted-by":"crossref","unstructured":"Feinberg B (1989) Coercion functions and decentralized linear programming. Math Oper Res 177\u2013187","DOI":"10.1287\/moor.14.1.177"},{"key":"171_CR23","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1080\/02331930310001611510","volume":"52","author":"G Feng","year":"2003","unstructured":"Feng G, Cui Z (2003) Combination of trust region method and simplicial decomposition for convex constrained nonlinear optimization. Optimization 52:459\u2013466","journal-title":"Optimization"},{"key":"171_CR24","first-page":"43","volume":"6","author":"G Feng","year":"2001","unstructured":"Feng G, Li M (2001) Quadratic approximation in the restricted simplicial decomposition. OR Trans 6:43\u201349","journal-title":"OR Trans"},{"key":"171_CR25","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1137\/S1052623499357258","volume":"13","author":"R Fletcher","year":"2002","unstructured":"Fletcher R, Gould NIM, Leyffer S, Toint PL, W\u00e4chter A (2002) Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. SIAM J Optim 13:635\u2013659","journal-title":"SIAM J Optim"},{"key":"171_CR26","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s101070100244","volume":"91","author":"R Fletcher","year":"2002","unstructured":"Fletcher R, Leyffer S (2002) Nonlinear programming without a penalty function. Math Program 91:239\u2013269","journal-title":"Math Program"},{"key":"171_CR27","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1287\/mnsc.5.1.97","volume":"5","author":"LR Ford Jr","year":"1958","unstructured":"Ford LR Jr, Fulkerson DR (1958) A suggested computation for maximal multi-commodity network flows. Manag Sci 5:97\u2013101","journal-title":"Manag Sci"},{"key":"171_CR28","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1002\/nav.3800030109","volume":"3","author":"M Frank","year":"1956","unstructured":"Frank M, Wolfe P (1956) An algorithm for quadratic programming. Nav Res Logist Q 3:95\u2013110","journal-title":"Nav Res Logist Q"},{"key":"171_CR29","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.ejor.2007.02.001","volume":"185","author":"JD Fuller","year":"2008","unstructured":"Fuller JD, Chung W (2008) Benders decomposition for a class of variational inequalities. Eur J Oper Res 185:76\u201391","journal-title":"Eur J Oper Res"},{"key":"171_CR30","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1080\/0233193031000079856","volume":"52","author":"R Garc\u00eda","year":"2003","unstructured":"Garc\u00eda R, Mar\u00edn A, Patriksson M (2003) Column generation algorithms for nonlinear optimization, I: convergence analysis. Optimization 52:171\u2013200","journal-title":"Optimization"},{"key":"171_CR31","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.cor.2010.07.021","volume":"38","author":"R Garc\u00eda","year":"2011","unstructured":"Garc\u00eda R, Mar\u00edn A, Patriksson M (2011) Column generation algorithms for nonlinear optimization, II: numerical investigations. Comput Oper Res 38:591\u2013604","journal-title":"Comput Oper Res"},{"key":"171_CR32","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1287\/mnsc.16.11.652","volume":"16","author":"AM Geoffrion","year":"1970","unstructured":"Geoffrion AM (1970) Elements of large scale mathematical programming. Manag Sci 16:652\u2013691","journal-title":"Manag Sci"},{"key":"171_CR33","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1287\/opre.9.6.849","volume":"9","author":"P Gilmore","year":"1961","unstructured":"Gilmore P, Gomory R (1961) A linear programming approach to the cutting stock problem. Oper Res 9:849\u2013859","journal-title":"Oper Res"},{"key":"171_CR34","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1287\/opre.11.6.863","volume":"11","author":"P Gilmore","year":"1963","unstructured":"Gilmore P, Gomory R (1963) A linear programming approach to the cutting stock problem\u2014part ii. Oper Res 11:863\u2013888","journal-title":"Oper Res"},{"key":"171_CR35","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1090\/S0002-9904-1964-11178-2","volume":"70","author":"AA Goldstein","year":"1964","unstructured":"Goldstein AA (1964) Convex programming in Hilbert space. Bull Am Math Soc 70:709\u2013710","journal-title":"Bull Am Math Soc"},{"key":"171_CR36","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","volume":"48","author":"PT Harker","year":"1990","unstructured":"Harker PT, Pang J-S (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math Program 48:161\u2013220","journal-title":"Math Program"},{"key":"171_CR37","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0191-2615(84)90017-1","volume":"18","author":"DW Hearn","year":"1984","unstructured":"Hearn DW, Lawphongpanich S, Nguyen S (1984) Convex programming formulations of the asymmetric traffic assignment problem. Transp Res B Methodol 18:357\u2013365","journal-title":"Transp Res B Methodol"},{"key":"171_CR38","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0167-6377(85)90016-1","volume":"4","author":"DW Hearn","year":"1985","unstructured":"Hearn DW, Lawphongpanich S, Ventura JA (1985) Finiteness in restricted simplicial decomposition. Oper Res Lett 4:125\u2013130","journal-title":"Oper Res Lett"},{"key":"171_CR39","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BFb0121181","volume":"31","author":"DW Hearn","year":"1987","unstructured":"Hearn DW, Lawphongpanich S, Ventura JA (1987) Restricted simplicial decomposition: computation and extensions. Math Program Study 31:99\u2013118","journal-title":"Math Program Study"},{"key":"171_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00941156","volume":"65","author":"JE Higgins","year":"1990","unstructured":"Higgins JE, Polak E (1990) Minimizing pseudoconvex functions on convex compact sets. J Optim Theory Appl 65:1\u201327","journal-title":"J Optim Theory Appl"},{"key":"171_CR41","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF01580219","volume":"6","author":"CA Holloway","year":"1974","unstructured":"Holloway CA (1974) An extension of the Frank and Wolfe method of feasible directions. Math Program 6:14\u201327","journal-title":"Math Program"},{"key":"171_CR42","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BF01585162","volume":"62","author":"KL Jones","year":"1993","unstructured":"Jones KL, Lustig IJ, Farvolden JM, Powell WB (1993) Multicommodity network flows: the impact of formulation on decomposition. Math Program 62:95\u2013117","journal-title":"Math Program"},{"key":"171_CR43","first-page":"99","volume":"4","author":"A Karakitsiou","year":"2004","unstructured":"Karakitsiou A, Mavrommati A, Migdalas A (2004) Efficient minimization over products of simplices and its application to nonlinear multicommodity network flows. Oper Res 4:99\u2013118","journal-title":"Oper Res"},{"key":"171_CR44","doi-asserted-by":"crossref","unstructured":"Kim K, Nazareth JL (1991) The decomposition principle and algorithms for linear programming. Linear Algebra Appl 152:119\u2013133","DOI":"10.1016\/0024-3795(91)90270-7"},{"key":"171_CR45","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1287\/trsc.26.1.4","volume":"26","author":"T Larsson","year":"1992","unstructured":"Larsson T, Patriksson M (1992) Simplicial decomposition with disaggregated representation for the traffic assignment problem. Transp Sci 26:4\u201317","journal-title":"Transp Sci"},{"key":"171_CR46","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF01582565","volume":"64","author":"T Larsson","year":"1994","unstructured":"Larsson T, Patriksson M (1994) A class of gap functions for variational inequalities. Math Program 64:53\u201379","journal-title":"Math Program"},{"key":"171_CR47","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/0191-2615(95)00016-7","volume":"29","author":"T Larsson","year":"1995","unstructured":"Larsson T, Patriksson M (1995) An augmented Lagrangian dual algorithm for link capacity side constrained traffic assignment problems. Transp Res B Methodol 29:433\u2013455","journal-title":"Transp Res B Methodol"},{"key":"171_CR48","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/S0191-2615(98)00024-1","volume":"33","author":"T Larsson","year":"1999","unstructured":"Larsson T, Patriksson M (1999) Side constrained traffic equilibrium models\u2014analysis, computation and applications. Transp Res B Methodol 33:233\u2013264","journal-title":"Transp Res B Methodol"},{"key":"171_CR49","unstructured":"Larsson T, Patriksson M, Rydergren C (1996) Applications of simplicial decomposition with nonlinear column generation to nonlinear network flows. In: Pardalos PM, Hearn DW, Hager WW (eds) Network optimization. Proceedings of the network optimization conference. Lecture notes in economics and mathematical systems, University of Florida, Gainesville, vol 450. Springer, Berlin, pp 346\u2013373"},{"key":"171_CR50","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0191-2615(02)00092-9","volume":"38","author":"T Larsson","year":"2004","unstructured":"Larsson T, Patriksson M, Rydergren C (2004) A column generation procedure for the side constrained traffic equilibrium problem. Transp Res B Methodol 38:17\u201338","journal-title":"Transp Res B Methodol"},{"key":"171_CR51","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/10556789808805688","volume":"9","author":"T Larsson","year":"1998","unstructured":"Larsson T, Patriksson M, Str\u00f6mberg A-B (1998) Ergodic convergence in subgradient optimization. Optim Methods Softw 9:93\u2013120","journal-title":"Optim Methods Softw"},{"key":"171_CR52","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1090\/conm\/568\/11282","volume":"568","author":"T Larsson","year":"2012","unstructured":"Larsson T, Patriksson M, Str\u00f6mberg A-B (2012) Ergodic convergence in subgradient optimization\u2014with application to simplicial decomposition of convex programs. Contemp Math 568:159\u2013189","journal-title":"Contemp Math"},{"key":"171_CR53","volume-title":"Optimization theory for large systems","author":"LS Lasdon","year":"1970","unstructured":"Lasdon LS (1970) Optimization theory for large systems. Macmillan, New York"},{"key":"171_CR54","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0167-6377(99)00059-0","volume":"26","author":"S Lawphongpanich","year":"2000","unstructured":"Lawphongpanich S (2000) Simplicial with truncated Dantzig\u2013Wolfe decomposition for nonlinear network flow problems with side constraints. Oper Res Lett 26:33\u201341","journal-title":"Oper Res Lett"},{"key":"171_CR55","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0191-2615(84)90026-2","volume":"18","author":"S Lawphongpanich","year":"1984","unstructured":"Lawphongpanich S, Hearn D (1984) Simplicial decomposition of the asymmetric traffic assignment problem. Transp Res B Methodol 18:123\u2013133","journal-title":"Transp Res B Methodol"},{"key":"171_CR56","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0041-5553(66)90114-5","volume":"6","author":"ES Levitin","year":"1966","unstructured":"Levitin ES, Polyak BT (1966) Constrained minimization methods. USSR Comput Math Math Phys 6:1\u201350","journal-title":"USSR Comput Math Math Phys"},{"key":"171_CR57","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1287\/opre.1050.0234","volume":"53","author":"ME L\u00fcbbecke","year":"2005","unstructured":"L\u00fcbbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53:1007\u20131023","journal-title":"Oper Res"},{"key":"171_CR58","volume-title":"Linear and nonlinear programming","author":"DG Luenberger","year":"1984","unstructured":"Luenberger DG (1984) Linear and nonlinear programming, 2nd edn. Addison-Wesley, Reading","edition":"2"},{"key":"171_CR59","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511983658","volume-title":"Mathematical programs with equilibrium constraints","author":"Z-Q Luo","year":"1996","unstructured":"Luo Z-Q, Pang J-S, Ralph D (1996) Mathematical programs with equilibrium constraints. Cambridge University Press, Cambridge"},{"key":"171_CR60","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1287\/mnsc.4.2.115","volume":"4","author":"AS Manne","year":"1958","unstructured":"Manne AS (1958) Programming of economic lot sizes. Manag Sci 4:115\u2013135","journal-title":"Manag Sci"},{"key":"171_CR61","doi-asserted-by":"crossref","unstructured":"Marcotte P, Dussault J-P (1989) A sequential linear programming algorithm for solving monotone variational inequalities. SIAM J Control Optim 27:1260\u20131278","DOI":"10.1137\/0327064"},{"key":"171_CR62","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1002\/net.3230260405","volume":"26","author":"A Mar\u00edn","year":"1995","unstructured":"Mar\u00edn A (1995) Restricted simplicial decomposition with side constraints. Networks 26:199\u2013215","journal-title":"Networks"},{"key":"171_CR63","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF01581701","volume":"65","author":"A Migdalas","year":"1994","unstructured":"Migdalas A (1994) A regularization of the Frank\u2013Wolfe method and unification of certain nonlinear programming methods. Math Program 65:331\u2013345","journal-title":"Math Program"},{"key":"171_CR64","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/j.ejor.2003.06.032","volume":"161","author":"E Mijangos","year":"2005","unstructured":"Mijangos E (2005) An efficient method for nonlinearly constrained networks. Eur J Oper Res 161:618\u2013635","journal-title":"Eur J Oper Res"},{"key":"171_CR65","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/0001-8708(69)90009-7","volume":"3","author":"U Mosco","year":"1969","unstructured":"Mosco U (1969) Convergence of convex sets and of solutions of variational inequalities. Adv Math 3:510\u2013585","journal-title":"Adv Math"},{"key":"171_CR66","first-page":"359","volume":"11","author":"JM Mulvey","year":"1990","unstructured":"Mulvey JM, Zenios SA, Ahlfeld DP (1990) Simplicial decomposition for convex generalized networks. J Inf Optim Sci 11:359\u2013387","journal-title":"J Inf Optim Sci"},{"key":"171_CR67","doi-asserted-by":"crossref","first-page":"1310","DOI":"10.1287\/mnsc.19.11.1310","volume":"19","author":"FH Murphy","year":"1973","unstructured":"Murphy FH (1973a) Column dropping procedures for the generalized programming algorithm. Manag Sci 19:1310\u20131321","journal-title":"Manag Sci"},{"key":"171_CR68","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1007\/BF01580134","volume":"5","author":"FH Murphy","year":"1973","unstructured":"Murphy FH (1973b) A column generation algorithm for nonlinear programming. Math Program 5:286\u2013298","journal-title":"Math Program"},{"key":"171_CR69","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.trb.2009.06.005","volume":"44","author":"Y Nie","year":"2009","unstructured":"Nie Y (2009) A class of bush-based algorithms for the traffic assignment problem. Transp Res B Methodol 44:73\u201389","journal-title":"Transp Res B Methodol"},{"key":"171_CR70","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/S0191-2615(03)00010-9","volume":"38","author":"Y Nie","year":"2004","unstructured":"Nie Y, Zhang HM, Lee D-H (2004) Models and algorithms for the traffic assignment problem with link capacity constraints. Transp Res B Methodol 38:285\u2013312","journal-title":"Transp Res B Methodol"},{"key":"171_CR71","volume-title":"Convex structures and economic theory","author":"H Nikaido","year":"1968","unstructured":"Nikaido H (1968) Convex structures and economic theory. Academic Press, New York"},{"key":"171_CR72","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1287\/mnsc.23.1.50","volume":"23","author":"RP O\u2019Neill","year":"1976","unstructured":"O\u2019Neill RP, Widhelm WB (1976) Acceleration of Lagrangian column-generation algorithms by penalty function methods. Manag Sci 23:50\u201358","journal-title":"Manag Sci"},{"key":"171_CR73","volume-title":"The traffic assignment problem\u2014Models and methods, VSP BV, Utrecht, The Netherlands, 1994","author":"M Patriksson","year":"1994","unstructured":"Patriksson M (1994) The traffic assignment problem\u2014Models and methods, VSP BV, Utrecht, The Netherlands. Facsimile republication 2015 by Dover Publications, Mineola, NY"},{"key":"171_CR74","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1137\/S105262349427577X","volume":"8","author":"M Patriksson","year":"1998","unstructured":"Patriksson M (1998a) Cost approximation: a unified framework of descent algorithms for nonlinear programs. SIAM J Optim 8:561\u2013582","journal-title":"SIAM J Optim"},{"key":"171_CR75","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/02331939808844409","volume":"44","author":"M Patriksson","year":"1998","unstructured":"Patriksson M (1998b) Cost approximation algorithms with nonmonotone line searches for nonlinear programs. Optimization 44:199\u2013217","journal-title":"Optimization"},{"key":"171_CR76","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1018358602892","volume":"9","author":"M Patriksson","year":"1998","unstructured":"Patriksson M (1998c) Decomposition methods for differentiable optimization problems on Cartesian product sets. Comput Optim Appl 9:5\u201342","journal-title":"Comput Optim Appl"},{"key":"171_CR77","series-title":"Vol. 23 of applied optimization","volume-title":"Nonlinear programming and variational inequality problems\u2014a unified approach","author":"M Patriksson","year":"1998","unstructured":"Patriksson M (1998d) Nonlinear programming and variational inequality problems\u2014a unified approach., Vol. 23 of applied optimization. Kluwer Academic Publishers, Dordrecht"},{"key":"171_CR78","volume-title":"Numerical methods in extremal problems","author":"BN Pshenichny","year":"1978","unstructured":"Pshenichny BN, Danilin YM (1978) Numerical methods in extremal problems. MIR Publishers, Moscow"},{"key":"171_CR79","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/BF01096416","volume":"3","author":"BN Pshenichnyi","year":"1993","unstructured":"Pshenichnyi BN, Sosnovsky AA (1993) The linearization method: principal concepts and perspective directions. J Glob Optim 3:483\u2013500","journal-title":"J Glob Optim"},{"key":"171_CR80","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton"},{"key":"171_CR81","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar RT (1976) Monotone operators and the proximal point algorithm. SIAM J Control Optim 14:877\u2013898","journal-title":"SIAM J Control Optim"},{"key":"171_CR82","volume-title":"Variational analysis","author":"RT Rockafellar","year":"1997","unstructured":"Rockafellar RT, Wets RJ-B (1997) Variational analysis. Springer, Berlin"},{"key":"171_CR83","volume-title":"Principles of mathematical analysis","author":"W Rudin","year":"1976","unstructured":"Rudin W (1976) Principles of mathematical analysis, 3rd edn. McGraw-Hill, Auckland","edition":"3"},{"key":"171_CR84","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0167-6377(89)90055-2","volume":"8","author":"A Ruszczy\u0144ski","year":"1989","unstructured":"Ruszczy\u0144ski A (1989) An augmented Lagrangian decomposition method for block diagonal linear programming problems. Oper Res Lett 8:287\u2013294","journal-title":"Oper Res Lett"},{"key":"171_CR85","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1137\/1021002","volume":"21","author":"G Salinetti","year":"1979","unstructured":"Salinetti G, Wets RJ-B (1979) On the convergence of sequences of convex sets in finite dimensions. SIAM Rev 21:18\u201333","journal-title":"SIAM Rev"},{"key":"171_CR86","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.amc.2008.09.014","volume":"206","author":"AH Shahpar","year":"2008","unstructured":"Shahpar AH, Aashtiani HZ, Babazadeh A (2008) Dynamic penalty function method for the side constrained traffic assignment problem. Appl Math Comput 206:332\u2013345","journal-title":"Appl Math Comput"},{"key":"171_CR87","unstructured":"Stefek D (1989) Extensions of simplicial decomposition for solving the multicommodity flow problem with bounded arc flows and convex costs. PhD thesis, University of Pennsylvania, Philadelphia, PN, USA"},{"key":"171_CR88","unstructured":"Str\u00f6mberg A-B (1997) Conditional subgradient methods and ergodic convergence in nonsmooth optimization. PhD thesis, Department of Mathematics, Link\u00f6ping Institute of Technology, Link\u00f6ping, Sweden"},{"key":"171_CR89","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF01581238","volume":"59","author":"JA Ventura","year":"1993","unstructured":"Ventura JA, Hearn DW (1993) Restricted simplicial decomposition for convex constrained problems. Math Program 59:71\u201385","journal-title":"Math Program"},{"key":"171_CR90","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01681343","volume":"9","author":"B Hohenbalken von","year":"1975","unstructured":"von Hohenbalken B (1975) A finite algorithm to maximize certain pseudo-concave functions on polytopes. Math Program 9:189\u2013206","journal-title":"Math Program"},{"key":"171_CR91","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF01584323","volume":"13","author":"B Hohenbalken von","year":"1977","unstructured":"von Hohenbalken B (1977) Simplicial decomposition in nonlinear programming algorithms. Math Program 13:49\u201368","journal-title":"Math Program"},{"key":"171_CR92","first-page":"1","volume-title":"Integer and nonlinear programming","author":"P Wolfe","year":"1970","unstructured":"Wolfe P (1970) Convergence theory in nonlinear programming. In: Abadie J (ed) Integer and nonlinear programming. Prentice-Hall, Englewood Cliffs, pp 1\u201336"},{"key":"171_CR93","volume-title":"Nonlinear programming: a unified approach","author":"WI Zangwill","year":"1969","unstructured":"Zangwill WI (1969) Nonlinear programming: a unified approach. Prentice-Hall, Englewood Cliffs"},{"key":"171_CR94","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/0377-2217(95)90601-A","volume":"83","author":"SA Zenios","year":"1995","unstructured":"Zenios SA, P\u0131nar M\u00c7, Dembo RS (1995) A smooth penalty function algorithm for network-structured problems. Eur J Oper Res 83:220\u2013236","journal-title":"Eur J Oper Res"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-015-0171-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12351-015-0171-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-015-0171-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:04:36Z","timestamp":1559462676000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12351-015-0171-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,8]]},"references-count":94,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["171"],"URL":"https:\/\/doi.org\/10.1007\/s12351-015-0171-3","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,8]]}}}