Tian, Guoqiang (1991): Generalized quasi-variational-like inequality problem. Published in: Mathematics of Operations Research , Vol. 18, No. 3 (August 1993): pp. 752-764.
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This paper gives some very general results on the generalized quasi-variational-like inequality problem. Since the problem includes all the existing extensions of the classical variational inequality problem as special cases, our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional. The approach adopted in this paper is based on continuous selection-type arguments and thus is quite different from the Berge Maximum Theorem or Hahn-Banach Theorem approach used in the literature.
|Item Type:||MPRA Paper|
|Original Title:||Generalized quasi-variational-like inequality problem|
|Keywords:||Quasi-Variational; Inequality; Problem|
|Subjects:||D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement|
|Depositing User:||Guoqiang Tian|
|Date Deposited:||13. Sep 2012 22:45|
|Last Modified:||18. Feb 2013 03:52|
 Allen, G. (1977). Variational Inequalities, Complementarity Problems, and Duality Theorems, J. Math. Anal. Appl. 58 1-10.
 Arrow, K. and Debreu, G. (1954). Existence of Equilibrium for a Competitive Economy. Economet- rica 22 265-290.
 Aubin, J. P. (1979). Mathematical Methods of Game and Economic Theory. North-Holland, Amster- dam, Holland.
 Ekeland, I. (1984). Applied Nonlinear Analysis. John Wiley & Sons, New York.
 Bergstrom, T. C., Parks, R. P. and Rader, T. (1976). Preferences Which Have Open Graphs. J. Math. Econom. 3 265-268.
 Chan, D. and Pang, J. S. (1982). The Generalized Quasi-Variational Inequality Problem. Math. Oper. Res. 7 211-222.
 Chang, S. and Zhang, Y. (1991). Generalized KKM Theorem and Variational Inequalities. J. Math. Anal. Appl. 159 208-223.
 Craven, B. D. (1981). Invex Functions and Constrained Local Minima. Bull. Austral. Math. Soc. 24 357-366.
 Debreu, G. (1952). A Social Equilibrium Existence Theorem. Proc. Nat. Acad. Sci. U.S.A. 38 386-393.
 Ding, X. P. and Tan, K.-K. (1990). Generalized Variational Inequalities and Generalized Quasi-Vari- ational Inequalities. J. Math. Anal. Appl. 148 497-508.
 Eilenberg, S. and Montgomery, D. (1946). Fixed Point Theorems for Multi-Valued Transformations. Amer. J. Math. 68 214-222.
 Fang, S. C. and Peterson, E. L. (1982). Generalized Variational Inequalities. J. Optim. Theory Appl. 38 363-383.
 Hanson, M. A. (1981). On Sufficiency of the Kuhn-Tucker Conditions. J. Math. Anal. Appl. 80 545-550.
 Hartman, P. T. and Stampacchia, G. (1966). On Some Nonlinear Ecliptic Differential Functional Equations. Acta Math. 115 153-188.
 Himmelberg, C. J. (1972). Fixed Points of Compact Multifunctions. J. Math. Anal. Appl. 38 205-207.
 Mangasarian, O. L. and Ponstein, J. (1965). Minimax and Duality in Nonlinear Programming. J. Math. Anal. Appl. 11 504-518.
 Michael, E. (1956). Continuous Selections. I. Ann. of Math. (2) 63 361-382.
 Mosco, U. (1976). Implicit Variational Problems and Quasi-Variational Inequalities. in Lecture Notes in Math. Vol. 543, 83-156, Springer Verlag, New York/Berlin.
 Parida, J. and Sen, A. (1987). A Variational-Like Inequality for Multifunctions with Applications. J. Math. Anal. Appl. 124 73-81.
 Saigal, R. (1976). Extension of the Generalized Complementarity Problem. Math. Oper. Res. 1 260-266.  Shih, M. H. and Tan, K. K. (1985). Generalized Quasi-Variational Inequalities in Locally Convex Topological Vector Spaces. J. Math. Anal. Appl. 108 333-343.
 Tian, G. (1991). Fixed Points Theorems for Mappings with Noncompact and Nonconvex Domains. J. Math. Anal. Appl. 158 160-167.
 (1992). Existence of Equilibrium in Abstract Economies with Discontinuous Payoffs and Noncompact Choice Spaces. J. Math. Econom. 21 379-388.
 (1992). Generalizations of the FKKM Theorem and Ky-Fan Minimax Inequality, with Applications to Maximal Elements, Price Equilibrium, and Complementarity. J. Math. Anal. Appl. 170 457-471.
 and Zhou, J. (1991). Quasi-Variational Inequalities with Noncompact Sets. J. Math. Anal. Appl. 160 583-595.
 Tian, G. (1991) and Zhou, J. (1993). Quasi-Variational Inequalities without Concavity Assumption Math. Anal. Appl. 172 289-299.
 Yannelis, N. C. (1987). Equilibria in Noncooperative Models of Competition. J. Econom. Theory 96-111.
 and Prabhakar, N. D. (1983). Existence of Maximal Elements and Equilibria in Lin Topological Spaces. J. Math. Econom. 12 233-245.
 Yao, J. C. (1991). The Generalized Quasi-Variational Inequality with Applications. J. Math. An Appl. 158 139-160.
 Zhou, J. X. and G. Chen, (1988). Diagonal Convexity Conditions for Problems in Convex Analy and Quasi-Variational Inequalities. J. Math. Anal. Appl. 132 213-225.
 and Tian, G. (1992). Transfer Method for Characterizing the Existence of Maximal Eleme of Binary Relations on Compact or Noncompact Sets. SIAM J. Control Optim. 2 360-375. G. Tian: Department of Economics, Texas A&M University, College Station, Texas 77843