Abstract
This paper studies some stability properties for the generalized quasivariational inequality problem. The study of this topic is motivated by the work of Harker and Pang (Ref. 1). A global stability result is obtained for problems satisfying certain conditions.
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Harker, P. T., andPang, J. S.,Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: Survey of Theory, Algorithms, and Applications, Mathematical Programming, Series B, Vol. 48, pp. 161–222, 1990.
Baiocchi, C., andCapelo, A.,Variational and Quasivariational Inequalities: Application to Free-Boundary Problems, Wiley, New York, New York, 1984.
Chen, D., andPang, J. S.,The Generalized Quasivariational Inequality Problem, Mathematics of Operations Research, Vol. 7, pp. 211–222, 1982.
Robinson, S. M.,Generalized Equations and Their Solutions, Mathematical Programming Studies, Vol. 10, pp. 128–141, 1979.
Qui, Y., andMagnanti, T. L.,Sensitivity Analysis for Variational Inequalities Defined on Polyhedral Sets, Working Paper No. OR-154-87, Operations Research Center, MIT, Cambridge, Massachusetts, 1987.
Qui, Y., andMagnanti, T. L.,Sensitivity Analysis for Variational Inequalities, Working Paper No. OR-163-87, Operations Research Center, MIT, Cambridge, Massachusetts, 1987.
Tobin, R. L.,Sensitivity Analysis for Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 48, pp. 191–204, 1986.
Kyparisis, J.,A Sensitivity Analysis Framework for Variational Inequalities, Mathematical Programming, Vol. 38, pp. 203–213, 1987.
Harker, P. T.,Generalized Nash Games and Quasi-Variational Inequalities, European Journal of Operational Research (to appear).
Marcott, P., andDussault, J. P.,A Note on a Globally Convergent Newton Method for Solving Monotone Variational Inequalities, Operations Research Letters, Vol. 6, pp. 35–42, 1987.
Mathiesen, L.,Computation of Economic Equalibria by a Sequence of Linear Complementarity Problems, Operations Research, Vol. 23, pp. 144–162, 1985.
Mathiesen, L.,Computational Experience in Solving Equilibrium Models by a Sequence of Linear Complementarity Problems, Operations Research, Vol. 33, pp. 1225–1250, 1985.
Fiacco, A. V.,Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, New York, 1983.
Hearn, D. W.,The Gap Function of a Convex Programming, Operations Research Letters, Vol. 1, pp. 67–71, 1982.
Marcott, P.,Gap-Decreasing Algorithms for Monotone Variational Inequalities, Paper Presented at the ORSA/TIMS Meeting, Miami Beach, Florida, 1986.
Harker, P. T., andPang, J. S.,Existence of Optimal Solutions to Mathematical Programs with Equilibrium Constraints, Operations Research Letters, Vol. 7, pp. 61–64, 1988.
McLinden, L.,Stable Monotone Variational Inequalities, Technical Summary Report No. 2734, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, 1984.
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Communicated by M. Avriel
The author would like to express his gratitude to the referees for helpful suggestions for the revision of the paper.
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Gong, L. Global stability result for the generalized quasivariational inequality problem. J Optim Theory Appl 70, 365–375 (1991). https://doi.org/10.1007/BF00940632
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DOI: https://doi.org/10.1007/BF00940632