We consider partial Browder-Tikhonov regularization techniques for variational inequality problems with P_0 cost mappings and box-constrained feasible sets. We present classes of economic equilibrium problems which satisfy such assumptions and propose a regularization method for these problems.
@article{bwmeta1.element.bwnjournal-article-amcv15i1p35bwm, author = {Konnov, Igor and Mazurkevich, Elena and Ali, Mohamed}, title = {On a regularization method for variational inequalities with P\_0 mappings}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {15}, year = {2005}, pages = {35-44}, zbl = {1084.49010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv15i1p35bwm} }
Konnov, Igor; Mazurkevich, Elena; Ali, Mohamed. On a regularization method for variational inequalities with P_0 mappings. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) pp. 35-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv15i1p35bwm/
[000] Baiocchi C. and Capelo A.(1984): Variational and Quasivariational Inequalities. Applications to Free Boundary Problems. - New York: Wiley. | Zbl 0551.49007
[001] Cottle R.W., Pang J.-S., and Stone R.E. (1992): The Linear Complementarity Problem. -Boston: Academic Press.
[002] Facchinei F. and Kanzow C. (1999): Beyond monotonicity in regularization methods for nonlinear complementarity problems. — SIAM J. Contr. Optim., Vol. 37, No. 4, pp. 1150–1161. | Zbl 0997.90085
[003] Facchinei F. and Pang J.-S. (2003): Finite-Dimensional Variational Inequalities and Complementarity Problems. - Berlin: Springer-Verlag. | Zbl 1062.90002
[004] Fiedler M. and Ptak V. (1962): On matrices with nonpositive off-diagonal elements and principal minors. - Czechoslovak Math. Journal, Vol. 12 (87), No. 3, pp. 382-400. | Zbl 0131.24806
[005] Kolstad C.D. and Mathiesen L.(1987): Necessary and sufficient conditions for uniqueness of a Cournot equilibrium. - Rev. Econ. Studies, Vol. 54, No. 4, pp. 681-690. | Zbl 0638.90014
[006] Konnov I.V. (2000): Properties of gap functions for mixed variational inequalities. - Siberian J. Numer. Math., Vol. 3, No. 3, pp. 259-270. | Zbl 1022.49006
[007] Konnov I.V. and Volotskaya E.O.(2002): Mixed variational inequalities and ecomonic equilibrium problems. - J. Appl. Math., Vol. 2, No. 6, pp. 289-314. | Zbl 1029.47043
[008] Manne A.S. (1985): On the formulation and solution of economic equilibrium models. - Math. Program. Study 23, Amsterdam: North-Holland, pp. 1-22. | Zbl 0575.90012
[009] More J. and Rheinboldt W.(1973): On P- and S-functions and related classes of n-dimensional nonlinear mappings. - Linear Alg. Appl., Vol. 6, No. 1, pp. 45-68. | Zbl 0247.65038
[010] Nagurney A. (1999): Network Economics: A Variational Inequality Approach. - Dordrecht: Kluwer. | Zbl 0873.90015
[011] Nikaido H. (1968): Convex Structures and Economic Theory. - New York: Academic Press. | Zbl 0172.44502
[012] Okuguchi K. and Szidarovszky F. (1990): The Theory of Oligipoly with Multi-Product Firms. - Berlin: Springer. | Zbl 0704.90001
[013] Ortega J.M. and Rheinboldt W.C. (1970): Iterative Solution of Nonlinear Equations in Several Variables. - New York: Academic Press. | Zbl 0241.65046
[014] Qi H.D. (1999): Tikhonov regularization for variational inequality problems. - J. Optim. Theory Appl., Vol. 102, No. 1, pp. 193-201. | Zbl 0939.90019