Quasi-Variational Inequalities and Applications to Equilibrium Problems with Elastic Demand
Part of the
Ettore Majorana International Science Series
book series (EMISS, volume 43)
Let (N, A, W) be a transportation network where N is the set of p nodes P i , i = 1, ...,p, A the set of directed arcs a i , i = 1 , ...,n, W the set of OD (origin-destination) pairs w j , j = 1, ...,ℓ. The flow on a i is denoted by f i and f denotes the column vector whose components are f i , i = 1, ..., n. The travel cost on arc a i is a given function of f which we denote by c i (f) and the column vector c(f), whose components are c i (f), denotes the travel cost on all arcs.
KeywordsVariational Inequality Column Vector Equilibrium Problem Travel Cost Elastic Demand
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M.J. Smith. “The existence, uniqueness and stability of traffic equilibrium”. Transpn. Res.
(1979), pp. 295–304.CrossRefGoogle Scholar
S.C. Dafermos. “Traffic equilibrium of variational inequalities”. Transportation Science
(1980), pp. 42–54.MathSciNetCrossRefGoogle Scholar
D.P. Bertsekas, E.M. Gafni. “Projection methods for variational inequality with application to the traffic assignment problem”. Math. Programming Study
(1982), pp. 139–151.MathSciNetCrossRefMATHGoogle Scholar
A. Maugeri. “Convex programming, variational inequalities and applications to the traffic equilibrium problem”. Appl. Math. Optim.
(1987), pp. 169–185.MathSciNetCrossRefMATHGoogle Scholar
S.C. Dafermos. “The general multinodal network equilibrium problem with elastic demand”. Networks
(1982), pp. 57–72.MathSciNetCrossRefMATHGoogle Scholar
M. Fukushima. “On the dual approach to the traffic assignment problem”. Transpn. Res.
, 18 B
(1984), pp. 235–245.Google Scholar
M. Fukushima, T. Itoh. “A dual approach to asymmetric traffic equilibrium problems”. Math. Japanica
(1987), pp. 701–721.MathSciNetMATHGoogle Scholar
U. Mosco. “Implicit variational problems and quasi-variational inequalities”. Lecture Notes in Mathematics
(1975), pp. 83–156.CrossRefGoogle Scholar
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