On a Regularization Method for Variational Inequalities with P₀ Mappings

• Autorzy: Konnov I. , Mazurkevich E. , Ali M.
• Języki publikacji: EN

Abstrakty

EN

We consider partial Browder-Tikhonov regularization techniques for variational inequality problems with P₀ 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.

Słowa kluczowe

EN

variational inequalitie; partial regularization approach; P0-mappings

PL

nierówność wariacyjna; metoda regularyzacji

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2005
• Tom: Vol. 15, no 1
• Strony: 35--44
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Konnov I.

• Department of Applied Mathematics, Kazan University, ul. Kremlevskaya 18, Kazan 420008, Russia

autor

Mazurkevich E.

• Informatics Problems Institute, Kazan 420012, Russia

autor

Ali M.

• Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

Bibliografia

• [1] Baiocchi C. and Capelo A. (1984): Variational and Quasivariational Inequalities. Applications to Free Boundary Problems. — New York: Wiley.
• [2] Cottle R.W., Pang J.-S., and Stone R.E. (1992): The Linear Complementarity Problem. — Boston: Academic Press.
• [3] 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.
• [4] Facchinei F. and Pang J.-S. (2003): Finite-Dimensional Variational Inequalities and Complementarity Problems. — Berlin: Springer-Verlag.
• [5] Fiedler M. and Pták V. (1962): On matrices with nonpositive off-diagonal elements and principal minors. — Czechoslovak Math. Journal, Vol. 12 (87), No. 3, pp. 382–400.
• [6] 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.
• [7] Konnov I.V. (2000): Properties of gap functions for mixed variational inequalities.—Siberian J. Numer. Math., Vol. 3, No. 3, pp. 259–270.
• [8] 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.
• [9] Manne A.S. (1985): On the formulation and solution of economic equilibrium models. — Math. Program. Study 23, Amsterdam: North–Holland, pp. 1–22.
• [10] Moré 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.
• [11] Nagurney A. (1999): Network Economics: A Variational Inequality Approach. — Dordrecht: Kluwer.
• [12] Nikaïdo H. (1968): Convex Structures and Economic Theory. — New York: Academic Press.
• [13] Okuguchi K. and Szidarovszky F. (1990): The Theory of Oligipoly with Multi-Product Firms. — Berlin: Springer.
• [14] Ortega J.M. and Rheinboldt W.C. (1970): Iterative Solution of Nonlinear Equations in Several Variables.— New York: Academic Press.
• [15] Qi H.D. (1999): Tikhonov regularization for variational inequality problems. — J. Optim. Theory Appl., Vol. 102, No. 1, pp. 193–201.