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Stampacchia generalized vector quasiequilibrium problems and vector saddle points. (English) Zbl 1103.49010
Summary: Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.

49J53Set-valued and variational analysis
Full Text: DOI
[1] GIANNESSI, F., Theorems of the Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley and Sons, New York, NY, pp. 151--186, 1980.
[2] GIANNESSI, F., Editor, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer Academic Publishers, Dordrecht, Netherlands, 2000. · Zbl 0952.00009
[3] GIANNESSI F., MASTROENI, G., and PELLEGRINI L., On the Theory of Vector Optimization and Variational Inequalities: Image Space Analysis and Separation, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Edited by F. Giannessi, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 153--215, 2000. · Zbl 0985.49005
[4] CHEN, G. Y., and YANG, X. Q., The Vector Complementarity Problem and Its Equivalence with the Weak Minimal Element in Ordered Spaces, Journal of Mathematical Analysis and Applications, Vol. 153, pp. 136--158, 1990. · Zbl 0719.90078 · doi:10.1016/0022-247X(90)90223-3
[5] CHEN, G. Y., and CRAVEN, B. D., A Vector Variational Inequality and Optimization over an Efficient Set, Zeitschrift für Operations Research, Vol. 341, pp. 1--12, 1990. · Zbl 0693.90091
[6] YANG, X. Q., Vector Complementarity and Minimal Element Problems, Journal of Optimization Theorem and Applications, Vol. 77, pp. 483--495, 1993. · Zbl 0796.49014 · doi:10.1007/BF00940446
[7] LEE, G. M., KIM, D. S., LEE B. S., and YEN, N. D., Vector Variational Inequality as a Tool for Studying Vector Optimization Problems, Nonlinear Analysis, Vol. 34, 745--765, 1998. · Zbl 0956.49007 · doi:10.1016/S0362-546X(97)00578-6
[8] DANIILIDIS, A., and HADJISAVVAS, N., Existence Theorems for Vector Variational Inequalities, Bulletin of the Australian Mathematical Society, Vol. 54, pp. 473--481, 1996. · Zbl 0887.49004
[9] BLUM, E., and OETTLI, W., From Optimization and Variational Inequalities to Equilibrium Problems, Mathematics Student, Vol. 63, pp. 123--145, 1994. · Zbl 0888.49007
[10] ANSARI, Q. H., KONNOV, I. V., and YAO, J.C., Characterizations of Solutions for Vector Equilibrium Problems, Journal of Optimization Theory and Applications, Vol. 113, pp. 435--447, 2002. · Zbl 1012.90055 · doi:10.1023/A:1015366419163
[11] ANSARI, Q.H., OETTLI, W., and SCHLÄGER, D., A Generalization of Vector Equilibria, Mathematical Methods of Operations Research, Vol. 46, pp. 147--152, 1997. · Zbl 0889.90155 · doi:10.1007/BF01217687
[12] BIANCHI, M., HADJISAVVAS, N., and SCHAIBLE, N., Vector Equilibrium Problems with Generalized Monotone Bifunctions, Journal of Optimization Theory and Applications, Vol. 92, pp. 527--542, 1997. · Zbl 0878.49007 · doi:10.1023/A:1022603406244
[13] FU, J.Y., Simultaneous Vector Variational Inequalities and Vector Implicit Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 93, pp. 141--151, 1997. · Zbl 0901.90169 · doi:10.1023/A:1022653918733
[14] FU, J. Y., and WAN, A. H., Generalized Vector Equilibrium Problems with Set-Valued Mappings, Mathematical Methods of Operations Research, Vol. 56, pp. 259--268, 2002. · Zbl 1023.90057 · doi:10.1007/s001860200208
[15] LUC, D. T., and VARGAS, C., A Saddlepoint Theorem for Set-Valued Maps, Nonlinear Analysis, Vol. 18, pp. 1--7, 1992. · Zbl 0797.90120 · doi:10.1016/0362-546X(92)90044-F
[16] FERRO, F., A Minimax Theorem for Vector-Valued Functions, Journal of Optimization Theory and Applications, Vol. 60, pp. 19--31, 1989. · Zbl 0631.90077 · doi:10.1007/BF00938796
[17] TAN, K. K., YU, J., and YUAN, X. Z., Existence Theorems for Saddle Points of Vector-Valued Maps, Journal of Optimization Theory and Applications, Vol. 89, pp. 731--747, 1996. · Zbl 0849.49009 · doi:10.1007/BF02275357
[18] YAO, J. C., The Generalized Quasivariational Inequality with Applications, Journal of Mathematical Analysis and Applications, Vol. 158, pp. 139--160, 1991. · Zbl 0739.49010 · doi:10.1016/0022-247X(91)90273-3
[19] AUBIN, J. P., and EKELAND, I., Aplied Nonlinear Analysis, Wiley, New York, NY, 1984.
[20] TAN, N. X., Quasivariational Inequalities in Topological Linear Locally Convex Hausdorft Spaces, Mathematische Nachrichten, Vol. 122, pp. 231--245, 1985. · doi:10.1002/mana.19851220123
[21] LIN, L. J., and YU, Z. T., On Some Equilibrium Problems for Multimaps, Journal of Computational and Applied Mathematics, Vol. 129, pp. 171--183, 2001. · Zbl 0990.49003 · doi:10.1016/S0377-0427(00)00548-3
[22] JAHN, J., Mathematical Vector Optimization in Partially-Ordered Linear Spaces, Peter Lang, Frankfurt, Germany, 1986. · Zbl 0578.90048
[23] FAN, K., A Minimax Inequality and Applications, Inequalities III, Edited by O. Shisha, Academic Press, New York, NY, pp. 103--113, 1972.
[24] GLICKSBERG, I., A Further Generalization of the Kakutani Fixed-Point Theorem with Application to Nash Equilibrium Points, Proceedings of the American Mathematical Society, Vol. 3, pp. 170--174, 1952. · Zbl 0046.12103
[25] CHEN, G. Y., YANG, X. Q., and, YU, H., A Nonlinear Scalarization Function and Generalized Quasivector Equilibrium Problems, Journal of Global Optimization (to appear).