Solving strongly monotone variational and quasi-variational inequalities

Discrete and Continuous Dynamical Systems

Volumn 31, Issue 4, 2011, Pages 1383-1396

  Nesterov, Yurii ^a   Scrimali, Laura ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITY OF CATANIA   (Italy)

Author keywords

Complexity analysis; Eficiency estimate; Monotone operators; Optimal methods; Quasi variational inequality; Variational inequality

Indexed keywords

EID: 84859541026     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2011.31.1383     Document Type: Conference Paper

References (32)

1. C. Baiocchi and A. Capelo, "Variational and Quasivariational Inequalities: Applications to Free Boundary Problems," A Wiley Interscience Publication, John Wiley & Sons, Inc., New York, 1984.
2. A. Bensoussan, M. Goursat and J.-L- Lions, Contrôle impulsionnel et inéquations quasi- variationnelle stationnaires, C. R. Acad. Sci. Paris Sér. A-B, 276 (1973), A1279-A1284.
3. A. Bensoussan, Points de Nash dans le cas de fontionnelles quadratiques et jeux differentiels linéaires à N personnes, SIAM J. Control, 12 (1974), 460-499.
4. M. Bliemer and P. Bovy, Quasi-variational inequality formulation of the multiclass dynamic trafic assignment problem, Transportation Res. Part B, 37 (2003), 501-519. (Pubitemid 36580170)
5. A. Causa and F. Raciti, Lipschitz continuity results for a class of variational inequalities and applications: A geometric approach, J. Optim. Theory Appl., 145 (2010), 235-248.
6. D. Chan and J. S. Pang, The generalized quasivariational inequality problem, Math. Oper. Res., 7 (1982), 211-222.
7. F. Facchinei and J. S. Pang, "Finite-Dimensional Variational Inequalities and Complementarity Problems," Springer Series in Operations Research, Springer-Verlag, New York, 2003.
8. M. Fukushima, Equivalent Differentiable optimization problems and descent methods for asymmetric variational inequality problems, Math. Program., 53 (1992), 99-110.
9. F. Giannessi, A. Maugeri and P. M. Pardalos, eds., "Variational Analysis and Applications," Kluwer Academic Publishers, 2005.
10. P. T. Harker, Generalized Nash games and quasi-variational inequalities, Eur. J. Oper. Res., 54 (1991), 81-94.
11. J. Haslinger, Aproximation of the Signorini problem with friction, obeying Coulomb law, Math. Methods Appl. Sci., 5 (1983), 422-437. (Pubitemid 14455899)
12. J. Haslinger and P. D. Panagiotopoulos, The reciprocal variational approach to the Sig- norini problem with friction. Approximation results, Proc. Royal Soc.of Edinburgh, Sect.A, 98 (1984), 365-383.
13. M. Kocvara and J. V. Outrata, On a class of quasi-variational inequalities, Optim. Methods Softw., 5 (1995), 275-295.
14. A. Maugeri and L. Scrimali, Global Lipschitz continuity of solutions to parameterized variational inequalities, Boll. Unione Mat. Ital. (9), 2 (2009), 45-69.
15. G. J. Minty, On the generalization of a direct method of the calculus of variations, Bull. Amer. Math. Soc., 73 (1967), 314-321.
16. U. Mosco, Implicit variational problems and quasi variational inequalities, in "Nonlinear Operators and Calculus of Variations" (Summer School, Univ. Libre Bruxelles, Brussels, 1975), Lectures Notes Math, 543, Springer, Berlin, (1976), 83-156.
17. A. Nagurney, "Network Economics: A Variational Inequality Approach," Advances in Computational Economics, 1, Kluwer Academic Publishers Group, Dordrecht, 1993.
18. A. Nemirovski, Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems, SIAM J. Optim., 15 (2004), 229-251. (Pubitemid 40360669)
19. A. Nemirovsky and D. Yudin, "Problem Complexity and Method Eficiency in Optimization," A Wiley Interscience Publication, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Inc., New York, 1983.
20. Yu. Nesterov, "Introductory Lectures on Convex Optimization. A Basic Course," Applied Optimization, 87, Kluwer Academic Publishers, Boston, MA, 2004.
21. Yu. Nesterov, Smooth minimization of nonsmooth function, Math. Program., 103 (2005), 127-152.
22. Yu. Nesterov, Dual extrapolation and its applications to solving variational inequalities and related problems, Math. Program., 109 (2007), 319-344. (Pubitemid 46197859)
23. Yu. Nesterov, Minimizing functions with bounded variation of the gradient, CORE DP 2005/79.
24. M. A. Noor and Z. A. Memon, Algorithms for general mixed quasi variational inequalities, J. Inequal. Pure Appl. Math., 3 (2002), 7 pp.
25. M. A. Noor and W. Oettli, On general nonlinear complementarity problems and quasiequilibria, Le Matematiche (Catania), 49, (1994) 313-331.
26. J. Outrata and J. Zowe, A numerical approach to optimization problems with variational inequality constraints, Math. Program., 68 (1995), 105-130.
27. J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria and multi-leader-follower games, Comput. Manag. Sci., 1 (2005), 21-56. (Pubitemid 40814996)
28. Salahuddin, Projection methods for quasi-variational inequalities, Mathematical and Computational Applications, 9 (2004), 125-131.
29. L. Scrimali, The ńancial equilibrium problem with implicit budget constraints, Cent. Eur. J. Oper. Res., 16 (2008), 191-203.
30. L. Scrimali, Mixed behavior network equilibria and quasi-variational inequalities, J. Ind. Manag. Optim., 5 (2009), 363-379.
31. J. C. Yao, The generalized quasi-variational inequality problem with applications, J. Math. Anal. Appl., 158 (1991), 139-160.
32. J. Y. Wei and Y. Smeers, Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices, Oper. Res., 47 (1999), 102-112. (Pubitemid 129700861)