{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,22]],"date-time":"2026-02-22T06:32:59Z","timestamp":1771741979911,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1985,6,1]],"date-time":"1985-06-01T00:00:00Z","timestamp":486432000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1985,6]]},"DOI":"10.1007\/bf02591749","type":"journal-article","created":{"date-parts":[[2007,3,29]],"date-time":"2007-03-29T15:42:12Z","timestamp":1175182932000},"page":"206-219","source":"Crossref","is-referenced-by-count":114,"title":["Asymmetric variational inequality problems over product sets: Applications and iterative methods"],"prefix":"10.1007","volume":"31","author":[{"given":"Jong-Shi","family":"Pang","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02591749_CR1","unstructured":"H.Z. Aashtiani, \u201cThe multi-modal traffic assignment problem\u201d, Ph.D. dissertation, Alfred P. Sloan School of Management, Massachusetts Institute of Technology (May, 1979)."},{"key":"BF02591749_CR2","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1137\/0602024","volume":"2","author":"H.Z. Aashtiani","year":"1981","unstructured":"H.Z. Aashtiani and T.L. Magnanti, \u201cEquilibria on a congested transportation network\u201d,SIAM Journal on Algebraic and Discrete Methods 2 (1981) 213\u2013226.","journal-title":"SIAM Journal on Algebraic and Discrete Methods"},{"key":"BF02591749_CR3","volume-title":"Computation of market equilibria for policy analysis: The project independence evaluation system (PIES) approach","author":"B.H. Ahn","year":"1979","unstructured":"B.H. Ahn,Computation of market equilibria for policy analysis: The project independence evaluation system (PIES) approach (Garland Publishing Inc., New York 1979)."},{"key":"BF02591749_CR4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1287\/opre.30.2.281","volume":"30","author":"B.H. Ahn","year":"1982","unstructured":"B.H. Ahn and W.W. Hogan, \u201cOn convergence of the PIES algorithm for computing equilibria\u201d,Operations Research 30 (1982) 281\u2013300.","journal-title":"Operations Research"},{"key":"BF02591749_CR5","doi-asserted-by":"crossref","unstructured":"R.L. Asmuth, \u201cTraffic network equilibria\u201d, Technical Report SOL 78-2, Systems Optimization Laboratory, Department of Operations Research, Stanford University (January, 1978).","DOI":"10.21236\/ADA054268"},{"key":"BF02591749_CR6","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1287\/moor.4.3.209","volume":"4","author":"R.L. Asmuth","year":"1979","unstructured":"R.L. Asmuth, B.C. Eaves and E.L. Peterson, \u201cComputing economic equilibria on affine networks with Lemke\u2019s algorithm\u201d,Mathematics of Operations Research 4 (1979) 209\u2013214.","journal-title":"Mathematics of Operations Research"},{"key":"BF02591749_CR7","unstructured":"R.W. Cottle and S.G. Duvall, \u201cA Lagrangean relaxation algorithm for the constrained matrix problem\u201d, Technical report SOL 82-10, Systems Optimization Laboratory, Department of Operations Research, Stanford University (July 1982)."},{"key":"BF02591749_CR8","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1287\/trsc.14.1.42","volume":"14","author":"S.C. Dafermos","year":"1980","unstructured":"S.C. Dafermos, \u201cTraffic equilibrium and variational inequalities\u201d,Transportation Science 14 (1980) 42\u201354.","journal-title":"Transportation Science"},{"key":"BF02591749_CR9","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1287\/trsc.16.2.231","volume":"16","author":"S.C. Dafermos","year":"1982","unstructured":"S.C. Dafermos, \u201cRelaxation algorithms for the general asymmetric traffic equlibrium problem\u201d,Transportation Science 16 (1982) 231\u2013240.","journal-title":"Transportation Science"},{"key":"BF02591749_CR10","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/BF02591891","volume":"26","author":"S.C. Dafermos","year":"1983","unstructured":"S.C. Dafermos, \u201cAn iterative scheme for variation inequalities\u201d,Mathematical Programming 26 (1983) 40\u201347.","journal-title":"Mathematical Programming"},{"key":"BF02591749_CR11","series-title":"Mathematics Research Report","volume-title":"Economic equilibria on networks","author":"S.C. Fang","year":"1980","unstructured":"S.C. Fang and E.L. Peterson, \u201cEconomic equilibria on networks\u201d, Mathematics Research Report 80-13, Department of Mathematics, University of Maryland, Baltimore County (1980)."},{"key":"BF02591749_CR12","unstructured":"M. Florian, \u201cAsymmetric variable demand multi-modal traffic equilibrium problems: Existence, uniqueness and a solution algorithm\u201d, Publication No. 152, Centre de Recherche sur les Transports, Universit\u00e9 de Montr\u00e9al (October 1979)."},{"key":"BF02591749_CR13","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/0191-2615(82)90007-8","volume":"16B","author":"M. Florian","year":"1982","unstructured":"M. Florian and H. Spiess, \u201cThe convergence of diagnoalization algorithms for asymmetric network equilibrium problems\u201d,Transportation Research 16B (1982) 477\u2013483.","journal-title":"Transportation Research"},{"key":"BF02591749_CR14","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1111\/j.1467-9787.1983.tb00994.x","volume":"23","author":"T.L. Friesz","year":"1983","unstructured":"T.L. Friesz, R.L. Tobin, T.E. Smith and P.T. Harker, \u201cA nonlinear complementarity formulation and solution procedure for the general derived demand network equilibrium problem\u201d,Journal of Regional Science 23 (1983) 337\u2013359.","journal-title":"Journal of Regional Science"},{"key":"BF02591749_CR15","first-page":"271","volume-title":"Applied stochastic control in econometrics and management science","author":"D. Gabay","year":"1980","unstructured":"D. Gabay and H. Moulin, \u201cOn the uniqueness and stability of Nash-equilibria in noncooperative games\u201d, in A. Bensoussan, P. Kleindorfer and C.S. Tapiero, eds.,Applied stochastic control in econometrics and management science (North-Holland, Amsterdam 1980) 271\u2013293."},{"key":"BF02591749_CR16","unstructured":"P.T. Harker, \u201cA variational inequality aproach for the determination of oligopolistic market equilibrium\u201d, to appear inMathematical Programming."},{"key":"BF02591749_CR17","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1090\/psapm\/021\/483658","volume":"21","author":"W.W. Hogan","year":"1977","unstructured":"W.W. Hogan, \u201cProject independence evaluation system: Structure and algorithms\u201d,Proceedings of Symposia in Applied Mathematics 21 (1977) 121\u2013137.","journal-title":"Proceedings of Symposia in Applied Mathematics"},{"key":"BF02591749_CR18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF00930577","volume":"4","author":"S. Karamardian","year":"1969","unstructured":"S. Karamardian, \u201cThe nonlinear complementarity problem with applications, Part 2\u201d,Journal of Optimization Theory and Applications 4 (1969) 167\u2013181.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"BF02591749_CR19","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF00932464","volume":"8","author":"S. Karamardian","year":"1971","unstructured":"S. Karamardian, \u201cGeneralized complementarity problem\u201d,Journal of Optimization Theory and Applications 8 (1971) 161\u2013168.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"BF02591749_CR20","volume-title":"An introduction to variational inequalities and their applications","author":"D. Kinderlehrer","year":"1980","unstructured":"D. Kinderlehrer and G. Stampacchia,An introduction to variational inequalities and their applications (Academic Press, New York, 1980)."},{"key":"BF02591749_CR21","unstructured":"S. Lawphongpanich and D.W. Hearn, \u201cSimplicial decomposition of the asymmetric traffic assignment problem\u201d, to appear inTransportation Research."},{"key":"BF02591749_CR22","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1111\/j.1467-9787.1976.tb00976.x","volume":"16","author":"J.G. MacKinnon","year":"1976","unstructured":"J.G. MacKinnon, \u201cA technique for the solution of spatial equilibrium models\u201d,Journal of Regional Science 16 (1976) 293\u2013307.","journal-title":"Journal of Regional Science"},{"key":"BF02591749_CR23","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/0022-247X(72)90043-1","volume":"40","author":"U. Mosco","year":"1972","unstructured":"U. Mosco, \u201cDual variational inequalities\u201d, Journal ofMathematical Analysis and Applications 40 (1972) 202\u2013206.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"BF02591749_CR24","volume-title":"Iterative solution of nonlinear equations in several variables","author":"J.M. Ortega","year":"1970","unstructured":"J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970)."},{"key":"BF02591749_CR25","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1287\/mnsc.27.10.1142","volume":"27","author":"J.S. Pang","year":"1981","unstructured":"J.S. Pang, \u201cA hybrid method for the solution of some multi-commodity spatial equilibrium problems\u201d,Management Science 27 (1981) 1142\u20131157.","journal-title":"Management Science"},{"key":"BF02591749_CR26","unstructured":"J.S. Pang, \u201cSolution of the general multi-commodity spatial equilibrium problem by variational and complementarity methods\u201d, to appear inJournal of Regional Science."},{"key":"BF02591749_CR27","unstructured":"J.S. Pang, \u201cMore results on the convergence of iterative methods for the symmetric linear complementarity problem\u201d, to appear injournal of Optimization Theory and Applications."},{"key":"BF02591749_CR28","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1007\/BF01585112","volume":"24","author":"J.S. Pang","year":"1982","unstructured":"J.S. Pang and D. Chan, \u201cIterative methods for variational and complementarity problems\u201d,Mathematical Programming 24 (1982) 284\u2013313.","journal-title":"Mathematical Programming"},{"key":"BF02591749_CR29","unstructured":"J.S. Pang and D. Chan, \u201cGauss-Seidel methods for variational inequality problems over product sets\u201d, unpublished manuscript, School of Management, University of Texas at Dallas (1982)."},{"key":"BF02591749_CR30","unstructured":"J.S. Pang and C.S. Yu, \u201cLinearized simplicial decomposition methods for computing traffic equlibria on networks\u201d, to appear inNetworks."},{"key":"BF02591749_CR31","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/BF02612715","volume":"28","author":"G. Pierra","year":"1984","unstructured":"G. Pierra, \u201cDecomposition through formalization in a product space\u201d,Mathematical Programming 28 (1984) 96\u2013115.","journal-title":"Mathematical Programming"},{"key":"BF02591749_CR32","volume-title":"Mathematical programming: The state of the art","author":"S.M. Robinson","year":"1983","unstructured":"S.M. Robinson, \u201cGeneralized equations\u201d, in: A. Bachem, M. Gr\u00f6tschel and B. Korte, eds.,Mathematical programming: The state of the art (Springer-Verlag, New York 1983)."},{"key":"BF02591749_CR33","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0166-0462(81)90023-5","volume":"11","author":"J. Rowse","year":"1981","unstructured":"J. Rowse, \u201cSolving the generalized transportation problem\u201d,Regional Science and Urban Economics 11 (1981) 57\u201368.","journal-title":"Regional Science and Urban Economics"},{"key":"BF02591749_CR34","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0191-2615(79)90022-5","volume":"13B","author":"M.J. Smith","year":"1979","unstructured":"M.J. Smith, \u201cExistence, uniqueness and stability of traffic equilibria\u201d,Transportation Research 13B (1979) 295\u2013304.","journal-title":"Transportation Research"},{"key":"BF02591749_CR35","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.1467-9787.1983.tb00795.x","volume":"23","author":"R.L. Tobin","year":"1983","unstructured":"R.L. Tobin and T.L. Friesz, \u201cFormulating and solving the spatial price equilibrium problem with transshipment in terms of arc variables\u201d,Journal of Regional Science 23 (1983) 187\u2013198.","journal-title":"Journal of Regional Science"},{"key":"BF02591749_CR36","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1680\/ipeds.1952.11259","volume":"1","author":"J.G. Wardrop","year":"1952","unstructured":"J.G. Wardrop, \u201cSome theoretical aspects of road traffic research\u201d,Proceedings of the Institute of Civil Engineers Part 2, 1 (1952) 325\u2013378.","journal-title":"Proceedings of the Institute of Civil Engineers Part 2"},{"key":"BF02591749_CR37","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1007\/BF01584249","volume":"21","author":"W.I. Zangwill","year":"1981","unstructured":"W.I. Zangwill and C.B. Garcia, \u201cEquilibrium programming: The path following approach and dynamics\u201d,Mathematical Programming 21 (1981) 262\u2013289.","journal-title":"Mathematical Programming"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02591749.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02591749\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02591749","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T23:37:49Z","timestamp":1558395469000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02591749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,6]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1985,6]]}},"alternative-id":["BF02591749"],"URL":"https:\/\/doi.org\/10.1007\/bf02591749","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,6]]}}}