{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,18]],"date-time":"2025-05-18T06:05:52Z","timestamp":1747548352546},"reference-count":48,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5762,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1991,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this article, we consider an asymmetric market disequilibrium model in a spatial setting in the case of rigid prices and\/or controls. In this problem, the markets need no longer clear. We show that the disequilibrium problem can be reformulated as an equilibrium problem over an abstract network with special structure. We then propose a network decomposition algorithm for the computation of the solution that exploits the structure and establishes convergence results using the theory of variational inequalities. Our computational results demonstrate the suitability of this approach for large\u2010scale market problems.<\/jats:p>","DOI":"10.1002\/net.3230210108","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T10:23:22Z","timestamp":1178965402000},"page":"109-132","source":"Crossref","is-referenced-by-count":29,"title":["A network equilibrium formulation of market disequilibrium and variational inequalities"],"prefix":"10.1002","volume":"21","author":[{"given":"Anna","family":"Nagurney","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lan","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0602024"},{"key":"e_1_2_1_3_2","unstructured":"M. Z.AashtianiandT. L.Magnanti A linearization and decomposition algorithm for computing urban traffic equilibria.Proceedings of the 1982 IEEE International Large Scale Systems Symposium(1982)8\u201319."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.4.3.209"},{"key":"e_1_2_1_5_2","volume-title":"Studies in the Economics of Transportation","author":"Beckmann M. J.","year":"1956"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1983.1103183"},{"key":"e_1_2_1_7_2","volume-title":"Data Networks","author":"Bertsekas D.","year":"1987"},{"key":"e_1_2_1_8_2","volume-title":"Parallel and Distributed Computation","author":"Bertsekas D. P.","year":"1989"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1974.223806"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.14.1.42"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230120105"},{"key":"e_1_2_1_12_2","first-page":"57","article-title":"An iterative scheme for variational inequalities","volume":"28","author":"Dafermos S.","year":"1983","journal-title":"Math. Program."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-0462(86)90004-9"},{"key":"e_1_2_1_14_2","series-title":"NATO ASI Series, Series F: Computer and Systems Sciences","volume-title":"Flow Control of Congested Networks","author":"Dafermos S.","year":"1987"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.32.5.1069"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02612357"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(84)90055-5"},{"key":"e_1_2_1_18_2","unstructured":"S.DafermosandA.Nagurney Isomorphism between spatial price and traffic network equilibrium models. LCDS #85\u201017 Brown University Providence RI (1985)."},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.23.2.118"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.073B.010"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00436510"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.17.4.454"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.11.2.166"},{"key":"e_1_2_1_24_2","doi-asserted-by":"crossref","unstructured":"M.Florian An improved linear approximation algorithm for the network equilibrium (packet switching) problem.IEEE Proceed. Decision Control(1977)812\u2013818.","DOI":"10.1109\/CDC.1977.271681"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-0462(82)90008-4"},{"key":"e_1_2_1_26_2","first-page":"477","article-title":"The convergence of diagonalization algorithms for asymmetric network equilibrium problems","volume":"16","author":"Florian M.","year":"1982","journal-title":"Trans. Sci."},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230030202"},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9787.1984.tb01043.x"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591861"},{"key":"e_1_2_1_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/0191-2615(85)90013-X"},{"key":"e_1_2_1_31_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9787.1987.tb01144.x"},{"key":"e_1_2_1_32_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9787.1987.tb01144.x"},{"key":"e_1_2_1_33_2","doi-asserted-by":"publisher","DOI":"10.1068\/a210099"},{"key":"e_1_2_1_34_2","doi-asserted-by":"publisher","DOI":"10.1080\/08823871.1989.10462378"},{"key":"e_1_2_1_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(88)90412-8"},{"key":"e_1_2_1_36_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230190703"},{"key":"e_1_2_1_37_2","doi-asserted-by":"publisher","DOI":"10.1177\/109434208900300104"},{"key":"e_1_2_1_38_2","article-title":"Disequilibrium and variational inequalities","author":"Nagurney A.","journal-title":"J. Comput. Appl. Maths"},{"key":"e_1_2_1_39_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591749"},{"key":"e_1_2_1_40_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585112"},{"key":"e_1_2_1_41_2","first-page":"283","article-title":"A spatial price equilibrium and linear programming","volume":"42","author":"Samuelson P. A.","year":"1952","journal-title":"Am. Econ. Rev."},{"key":"e_1_2_1_42_2","volume-title":"Urban Transportation Networks","author":"Sheffi Y.","year":"1985"},{"key":"e_1_2_1_43_2","first-page":"365","article-title":"An algorithm for solving asymmetric equilibrium problems with a continuous cost\u2010flow function","author":"Smith M.","year":"1979","journal-title":"Trans. Res."},{"key":"e_1_2_1_44_2","volume-title":"Spatial and Temporal Price and Allocation Models","author":"Takayama T.","year":"1971"},{"key":"e_1_2_1_45_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9787.1986.tb01068.x"},{"key":"e_1_2_1_46_2","doi-asserted-by":"crossref","unstructured":"J.Wardrop Some theoretical aspects of road traffic research.Proceedings of the Institute of Civil Engineers Part II Vol. 1 325\u2013378(1952).","DOI":"10.1680\/ipeds.1952.11259"},{"key":"#cr-split#-e_1_2_1_47_2.1","unstructured":"L.Zhao Variational inequalities in general equilibrium: Analysis and computation. Ph.D. Thesis Division of Applied Mathematics Brown University Providence RI (1989)"},{"key":"#cr-split#-e_1_2_1_47_2.2","unstructured":"also appears as LCDS\/CCS Report #88\u201024 Division of Applied Mathematics Brown University Providence RI (1988)."},{"key":"e_1_2_1_48_2","unstructured":"L.Zubieta Mod\u00e9les d'equilibre spatial et m\u00e9thodes de resolution. Ph.D. Thesis D\u00e9partment d'Informatique et de Recherche Op\u00e9rationnelle Universit\u00e9 de Montr\u00e9al Montr\u00e9al Quebec (1986)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230210108","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230210108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T00:55:54Z","timestamp":1698022554000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230210108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,1]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,1]]}},"alternative-id":["10.1002\/net.3230210108"],"URL":"https:\/\/doi.org\/10.1002\/net.3230210108","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,1]]}}}