Regularity results for time-dependent variational and quasi-variational inequalities and application to the calculation of dynamic traffic network

Mathematical Models and Methods in Applied Sciences

Volumn 17, Issue 2, 2007, Pages 277-304

  Barbagallo, Annamaria ^a  

^a UNIVERSITY OF CATANIA   (Italy)

Author keywords

Continuity of solutions; Dynamic traffic equilibrium problem; Mosco's convergence; Time dependent variational and quasi variational inequalities; Traffic equilibrium problems

Indexed keywords

EID: 33846989827     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202507001917     Document Type: Article

References (22)

1. S. Dafermos, Traffic equilibrium and variational inequalities, Transp. Sci. 14 (1980) 42-54.
2. P. Daniele, A. Maugeri and W. Oettli, Variational inequalities and time-dependent traffic equilibria, C. R. Acad. Sci. Paris 326 (1998) 1059-1062.
3. P. Daniele, A. Maugeri and W. Oettli, Time-dependent traffic equilibria, J. Optim. Theory Appl. 103 (1999) 543-554.
4. M. De Luca and A. Maugeri, Discontinuous quasi-variational inequalities and applications to equilibrium problems, in Nonsmooth Optimization Methods and Applications (Gordon & Breach, 1992), pp. 70-74.
5. T. L. Friesz, D. Bernstein, T. E. Smith, R. L. Tobin and B. W. Wie, A variational inequality formulation of the dynamic network user equilibrium problem, Oper. Res. 41 (1993) 179-191.
6. J. Gwinner, Time dependent variational inequalities. Some recent trends, in Equilibrium Problems and Variational Models, eds. P. Daniele, F. Giannesi and A. Maugeri (Kluwer, 2003), pp. 225-264.
7. P. T. Harker and J. S. Pang, Finite-dimensional variational inequality and nonlinear complementary problems: A survey of theory, algorithms and applications, Math. Program. 48 (1990) 161-220.
8. P. Marcotte and J. H. Wu, On the convergence of projection methods application to the decomposition of affine variational inqualities, J. Optim. Theory Appl. 85 (1995) 347-362.
9. A. Maugeri, Dynamic models and generalized equilibrium problems, in New Trends in Mathematical Programming, od. F. Giannessi (Kluwer, 1998), pp. 191-202.
10. A. Maugeri, W. Oettli and D. Schläger, A flexible form of Wardrop's principle for traffic equilibria with side constraints, Rend. Circ. Mat. Palermo (2) Suppl. 48 (1997) 185-193.
11. A. Maugeri and C. Vitanza, Time-dependent equilibrium problems, in Pareto Optimality Game Theory and Equilibria, eds. A. Migdalos, P. Pardalos and L. Pitsoulis, (Springer, 2006).
12. U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Adv. Math. 3 (1969) 510-585.
13. A. Nagurney, Network Economics: A Variational Inequality Approach (Kluwer, 1993).
14. M. Patriksson, Nonlinear Programming and Variational Inequality Problems, A Unified Approach, Applied Optimization, Vol. 23 (Kluwer, 1999).
15. F. Raciti and L. Scrimali, Time-dependent variational inequalities and applications to equilibrium problems, J. Global Optim. 28 (2004) 387-400.
16. J. F. Rodrigues, Obstacle Problems in Mathematical Physics (North-Holland, 1987).
17. L. Scrimali, Quasi-variational inequalities in transportation networks, Math. Mod. Meth. Appl. Sci. 14 (2004) 1541-1560.
18. M. Sibony, Méthodes itératives pour les équations et inéquations aux dérivés partielles nonlinéares de type monotone, Calcolo 7 (1970) 65-183.
19. M. J. Smith, The existence, uniqueness and stability of traffic equilibria, Transp. Res. 13 (1979) 295-304.
20. N. X. Tan, Quasi-variational inequality in topological linear locally convex Hausdorff spaces, Math. Nachr. 122 (1985) 231-245.
21. F. Tinti, Numerical solution for pseudomonotone variational inequality problems by extragradient methods. Variational analysis arid applications, Nonconvex Optim. Appl. 79 (2005) 1101-1128.
22. J. G. Wardrop, Some theoretical aspects of road traffic research, in Proc. Inst. of Civil Engrs. Part II (1952), pp. 325-378.