Dafermos, Stella An iterative scheme for variational inequalities. (English) Zbl 0506.65026 Math. Program. 26, 40-47 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 82 Documents MSC: 65K10 Numerical optimization and variational techniques 49M20 Numerical methods of relaxation type 49J40 Variational inequalities Keywords:iterative methods; convergence; complementarity problems; traffic equilibrium × Cite Format Result Cite Review PDF Full Text: DOI References: [1] H.Z. Aashtiani and T.L. Magnanti, ”Equilibria on a congested transportation network”,SIAM Journal on Algebraic and Discrete Methods 2 (1981) 213–226. · Zbl 0501.90033 · doi:10.1137/0602024 [2] B.H. Ahn,Computation of market equilibria for policy analysis: the project independence evaluation system (PIES) approach (Gurland, New York, 1979). [3] R. Asmuth, B.C. Eaves and E.L. Peterson, ”Computing economic equilibria on affine networks with Lemke’s algorithm”,Mathematics of Operations Research 4 (1979) 209–214. · Zbl 0443.90027 · doi:10.1287/moor.4.3.209 [4] A. Auslender, ”Problèmes de minimax via l’analyse convexe et les inégalités variationelles: theorie et algorithmes”, Lecture Notes in Economics and Mathematical Systems (Springer, New York, 1972). · Zbl 0251.90039 [5] D.P. Bertsekas and E.M. Gafni, ”Projection methods for variational inequalities with application to the traffic assignment problem”, Tech. Rept., Laboratory for Information and Decision Systems, M.I.T., Cambridge, MA (1980). · Zbl 0478.90071 [6] H. Brezis and M. Sibony, ”Méthodes d’approximation et d’iteration pour les opérateurs monotones”Archive for Rational Mechanics and Analysis 28 (1969) 59–82 · Zbl 0157.22501 · doi:10.1007/BF00281564 [7] R.E. Bruck, ”An iterative solution of a variational inequality for certain monotone operators in Hilbert space”,Bulletin of the American Mathematical Society 81 (1975) 890–892. · Zbl 0332.49005 · doi:10.1090/S0002-9904-1975-13874-2 [8] S. Dafermos, ”Traffic equilibrium and variational inequalities”,Transportation Science 14 (1980) 42–54. · doi:10.1287/trsc.14.1.42 [9] S. Dafermos, ”The general multimodal traffic equilibrium problem”,Networks, 12 (1982) 57–72. · Zbl 0478.90022 · doi:10.1002/net.3230120105 [10] S. Dafermos, ”Relaxation algorithms for the general asymmetric traffic equilibrium problem”,Transportation Science 16 (1982) 231–240. · doi:10.1287/trsc.16.2.231 [11] B.C. Eaves, ”A locally quadratically convergent algorithm for computing stationary points”, Tech. Rep., Department of Operations Research, Stanford University, Stanford, CA (1978). · Zbl 0458.65057 [12] R. Glowinski, J.L. Lions and R. Trémolières,Analyse numérique des inéquations variationelles, méthodes mathématiques de l’informatique (Bordas, Paris, 1976). [13] N.H. Josephy, ”Newton’s method for generalized equations”, Tech. Rept. 1965, Mathematics Research Center, University of Wisconsin, Madison, WI (1979). [14] S. Karamardian, ”Generalized complementarity problem”,Journal of Optimization Theory and Applications 8 (1971) 161–168. · doi:10.1007/BF00932464 [15] D. Kinderlehrer and G. Stampacchia,An introduction to variational inequalities and applications (Academic Press, New York, 1980). · Zbl 0457.35001 [16] R. Kluge. Nichtlineare Variationsungleichungen und Extremaufgaben; Theorie und Näherungsverfahren (Deutscher Verlag der Wissenchaften, Berlin 1979). · Zbl 0452.49001 [17] J.J. Moré, ”Coercivity Conditions in nonlinear complementarity problems”,SIAM Review 16 (1974) 1–15. · doi:10.1137/1016001 [18] M.J. Smith, ”Existence, uniqueness and stability of traffic equilibria”,Transportation Research 13B (1979) 295–304. [19] T. Takayama and G.G. Judge,Spatial and temporal price and allocation models (North-Holland, Amsterdam, 1971). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.