A Survey on Vector Variational Inequalities
F. Giannessi; G. Matroeni; X. Q. Yang
Bollettino dell'Unione Matematica Italiana (2009)
- Volume: 2, Issue: 1, page 225-237
- ISSN: 0392-4041
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top- ANSARI, Q. H. - YAO, J. C., On nondifferentiable and nonconvex Vector Optimization Problems. J. Optim. Theory Appl., 106, no. 3 (2000), 475-488. Zbl0970.90092MR1797370DOI10.1023/A:1004697127040
- BROWDER FELIX, E., Existence and approximation of solutions of nonlinear variational inequalities. Proc. Nat. Acad. Sci. U.S.A., 56 (1966), 1080-1086. Zbl0148.13502MR203534DOI10.1073/pnas.56.4.1080
- CHEN, G. Y. - CHENG, G. M., Vector Variational Inequality and Vector Optimization, In "Lecture Notes in Econ. and Mathem. Systems", 285 (Springer-Verlag, New York-Berlin, 1987), 408-416.
- CHEN, G. Y., - HUANG, X. X. - YANG, X. Q., Vector optimization. Set-valued and variational analysis. Lecture Notes in Economics and Mathematical Systems, 541 (Springer-Verlag, Berlin, 2005). Zbl1104.90044MR2164220
- CHEN, G. Y. - YANG, X. Q., The vector complementary problem and its equivalences with vector minimal element in ordered spaces. J. Math. Anal. Appl., 153 (1990), 136-158. Zbl0712.90083MR1080123DOI10.1016/0022-247X(90)90270-P
- CHEN, G. Y. - YEN, N. D., On the variational inequality model for network equilibrium. Internal Report, Department of Mathematics, University of Pisa, no. 3 (1993), 196 (724).
- CRESPI, G. P. - GINCHEV, I. and ROCCA, M., Minty vector variational inequality, efficiency and proper efficiency. (English summary) Vietnam J. Math., 32, no. 1 (2004), 95-107. Zbl1056.49009MR2052725
- FANG, Y. P. - HUANG, N. J., Least element problems of feasible sets for vector F-complementarity problems with pseudomonotonicity. (Chinese) Acta Math. Sinica, 48, no. 3 (2005), 499-508. Zbl1124.90351MR2160727
- FANG, Y. P. - HUANG, N. J., Strong vector variational inequalities in Banach spaces. Applied Mathematics Letters, 19 (2006), 362-368. Zbl1138.49300MR2206227DOI10.1016/j.aml.2005.06.008
- GIANNESSI, F., Theorems of alternative, quadratic programs and complementary problems. In Cottle R. W. and Giannessi F. and Lions J. L. (eds.), Variational Inequality and Complementary Problems (Wiley, New York1980). Zbl0484.90081MR578747
- GIANNESSI, F., On Minty variational principle. In New Trends in Mathematical Programming (Kluwer Academic Publishers, 1998), 93-99. Zbl0909.90253MR1641312DOI10.1007/978-1-4757-2878-1_8
- F. GIANNESSI (ed.), Vector Variational Inequalities and Vector Equilibria. Kluwer Academic Publishers, Dordrecht, Boston, London, 2000. Zbl0952.00009MR1789109DOI10.1007/978-1-4613-0299-5
- HARKER, P. T. - PANG, J. S., Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Programming (Ser. B), 48, no. 2 (1990), 161-220. Zbl0734.90098MR1073707DOI10.1007/BF01582255
- HUANG, N. J. - FANG, Y. P., Strong vector F-complementary problem and least element problem of feasible set. Nonlinear Anal., 61, no. 6 (2005), 901-918. Zbl1135.90411MR2131786DOI10.1016/j.na.2005.01.021
- KINDERLEHRER, D. - STAMPACCHIA, G., An introduction to variational inequalities and their applications. Academic Press, New York, 1980. Zbl0457.35001MR567696
- KONNOV, I. V. - YAO, J. C., On the generalized vector variational inequality problem. J. Math. Anal. Appl., 206, no. 1 (1997), 42-58. Zbl0878.49006MR1429278DOI10.1006/jmaa.1997.5192
- LASSONDE, MARC, On the use of KKM multifunctions in fixed point theory and related topics. J. Math. Anal. Appl., 97, no. 1 (1983), 151-201. Zbl0527.47037MR721236DOI10.1016/0022-247X(83)90244-5
- LEE, G. M. - KIM, D. S. - LEE, B. S. - CHEN, G. Y., Generalized Vector Variational Inequality and its duality for set-valued maps. Appl. Mathem. Lett., 11 (1998), 21-26. Zbl0940.49008MR1630760DOI10.1016/S0893-9659(98)00050-0
- LEE, G. M. - KIM, D. S. - LEE, B. S. - CHEN, G. Y., Vector variational inequality as a tool for studying vector optimization problems. Nonlinear Anal., 34, no. 5 (1998), 745-765. Zbl0956.49007MR1634819DOI10.1016/S0362-546X(97)00578-6
- MASTROENI, G., On Minty Vector Variational Inequality. In [12], 351-361. Zbl0998.49005MR1789128DOI10.1007/978-1-4613-0299-5_20
- MENG, K. W. - LI, S. J., Differential and sensitivity properties of gap functions for Minty vector variational inequalities. J. Math. Anal. Appl., 337, no. 1 (2008), 386-398. Zbl1120.49007MR2356078DOI10.1016/j.jmaa.2007.04.009
- MOSCO, U., Implicit variational problems and quasi variational inequalities. Nonlinear operators and the calculus of variations (Summer School, Univ. Libre Bruxelles, Brussels, 1975), Lecture Notes in Math., 543 (Springer, Berlin, 1976), 83-156. MR513202
- WARD, D. E. - LEE, G. M., On relations between Vector Optimization Problems and Vector Variational Inequalities. J. Optim. Theory Appl., 113, no. 3 (2002), 583-596. Zbl1022.90024MR1904240DOI10.1023/A:1015364905959
- YANG, X. M. - YANG, X. Q. - TEO, K. L., Some Remarks On Minty Vector Variational Inequality. J. Optim. Theory Appl., 121, no. 1 (2004), 193-201. Zbl1140.90492MR2062976DOI10.1023/B:JOTA.0000026137.18526.7a
- YANG, X. Q., Vector complementarity and minimal element problems. J. Optim. Theory Appl., 77, no. 3 (1993), 483-495. Zbl0796.49014MR1233298DOI10.1007/BF00940446
- YANG, X. Q., Vector variational inequalities and its duality. Nonl. Anal., TMA, 21 (1993), 867-877. MR1249666DOI10.1016/0362-546X(93)90052-T
- YANG, X. Q. - GOH, C. J., On vector variational inequalities: application to vector equilibria. J. Optim. Theory Appl., 95 (1997), 431-443. Zbl0892.90158MR1477369DOI10.1023/A:1022647607947
- YEN, N. D. - LEE, G. M., On monotone and strongly monotone Vector Variational Inequalities. In [12], 467-478. Zbl0993.49013MR1789136DOI10.1007/978-1-4613-0299-5_28