A solution differentiability result for evolutionary quasi-variational inequalities

Journal of Global Optimization

Volumn 40, Issue 1-3, 2008, Pages 417-425

  Scrimali, Laura ^a  

^a UNIVERSITY OF CATANIA   (Italy)

Author keywords

Evolutionary quasi variational inequalities; Metric projections; Network models

Indexed keywords

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

METRIC PROJECTIONS; NETWORK EQUILIBRIUM PROBLEMS; NETWORK MODELS;

EVOLUTIONARY ALGORITHMS;

EID: 38849141732     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-007-9189-2     Document Type: Conference Paper

References (23)

1. Baiocchi F. and Capelo A. (1984). Variational and Quasivariational Inequalities. Applications to free boundary problems. Wiley, New York
2. Bliemer M. and Bovy P. (2003). Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem. Transport. Res. B 37: 501-519
3. Brezis H. (1983). Analyse fonctionelle. Théorie et applications. Masson, New York
4. Cubiotti P. (1999). Generalized quasi-variational inequalities in infinite-dimensional normed spaces. J. Optim. Theory Appl. 92(3): 457-475
5. Daniele, P.: Dynamic networks and evolutionary variational inequalities. Edward Elgar Publishing (2006)
6. Fiacco A.V. and McCormick G.P. (1968). Nonlinear programming: sequential unconstrained minimization techniques. Wiley, New York
7. Kyparisis J. (1986). Uniqueness and differentiability of solutions of parametric nonlinear complementarity problems. Math. Program. 36: 105-113
8. Kyparisis J. (1990). Solution differentiability for variational inequalities. Math. Program. 48: 285-301
9. Maugeri, A., Scrimali, L.: On the differentiability of solutions to variational inequalities with long-term memory. to appear
10. Maugeri, A., Vitanza, C.: Time-dependent equilibrium problems. In: Migdalos, A., Pardalos, P., Pitsoulis, L. (eds.) Pareto Optimality Game Theory and Equilibria, Nonconvex Optimization and its Applications Series. Springer, New York (2005)
11. Mordukhovich B. (2006). Variational analysis and generalized differentiation. Springer, New York
12. Nesterov, Yu., Scrimali, L.: Solving strongly monotone variational and quasi-variational inequalities. CORE Discussion Papers (2006/107)
13. Noor M.A. and Oettli W. (1994). On general nonlinear complementarity problems and quasiequilibria. Le Matematiche XLIX(II): 313-331
14. Robinson S.M. (1981). Some continuity properties of polyhedral multifunctions. Math. Program. Study 1: 206-214
15. Robinson S.M. (1982). Generalized equations and their solutions, part II: applications to nonlinear programming. Math. Program. Study 19: 200-221
16. Robinson, S.M.: Implicit B-differentiability in generalized equations, Technical Summary Report 2854. Mathematics Research center, University of Wisconsin, Madison, WI (1985)
17. Robinson, S.M., Lu, S.: Solution continuity in variational conditions. J. Glob. Optim. to appear
18. Scrimali L. (2004). Quasi-variational inequalities in transportation networks. Math. Models Methods Appl. Sci. 14(10): 1541-1560
19. Scrimali, L.: The financial equilibrium problem with implicit budget constraints. to appear
20. Shapiro A. (1988). Sensitivity analysis of nonlinear programs and differentiability properties of metric projections. SIAM J. Control Optim. 26: 628-645
21. Shapiro A. (2005). Sensitivity analysis of parameterized variational inequalities. Math. Oper. Res. 30(1): 109-126
22. Steinbach J. (1998). On a variational inequality containing a memory term with an application in electro-chemical machining. J. Convex Anal. 5(1): 63-80
23. Yen N.D. (1995). Hölder continuity of solutions to a parametric variational inequality. Appl. Math. Optim. 31: 245-255