Abstract
In this paper, we study equivalent relations between vector variational inequalities for subdifferentials and nondifferentiable convex vector optimization problems. Futhermore, using the equivalent relations, we give existence theorems for solutions of convex vector optimization problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aubin, J. P. (1979), Applied Functional Analysis, John Wiley & Sons, Inc..
Aubin, J. P. (1993), Optima and Equilibria, Springer-Verlag, Berlin Hidelberg New York.
Baiocchi, C. and Capelo, A. (1994), Variational and Quasi-Variational Inequalities Applications to Free-boundary Problems,John Wiley.
Browder, F. E. (1968), The fixed point theory of multivalued mappings in topological vector space, Math. Ann., Vol. 177, pp. 284–301.
Chen, G. Y. and Craven, B. D. (1994), Existence and continuity of solutions for vector optimization, J. Optim. Theory Appl., Vol. 81, pp. 459–468.
Chen, G. Y. and Li, S. J. (1996), Existence of solutions for generalized vector quasivariational inequality, J. Optim. Theory Appl., Vol. 90, pp. 331–334.
Clarke, F. H. (1983), Optimization and Nonsmooth Analysis, Wiley-Interscience, New York.
Geoffrion, A. M. (1968), Properly efficiency and the theory of vector maximization, J. Math. Anal. Appl., Vol. 22, pp. 618–630.
Giannessi, F. (1980), Theorems of alternative, quadratic programs and complementarity problems, in Variational Inequalities and Complementarity Problems, edited by Cottle, R. W., Giannessi, F. and Lions, J. L., pp. 151–186, John Wiley and Sons, Chichester, England.
Giannessi, F. (1997), On Minty variational principle, in New Trends in Mathematical programming, Kluwer.
Jeyakumar, V. (1986), A generalization of a minimax theorem of Fan via a theorem of the alternative, J. Optim. Theory Appl., Vol. 48, pp. 525–533.
Konnov, I. V. and Yao, J. C. (1997), On the generalized vector variational inequality problem, J. Math. Anal. Appl., Vol. 206, pp. 42–58.
Lee, G. M., Lee, B. S. and Chang, S. S. (1996), On vector quasivariational inequalities, J. Math. Anal. Appl., Vol. 203, pp. 626–638.
Lee, G. M., Kim, D. S., Lee, B. S. and Yen, N. D. (1998), Vector variational inequality as a tool for studying vector optimization problems, Nonlinear Anal., Th. Meth. Appl., Vol. 34, pp. 745–765.
Lee, G. M., Kim, D. S. and Kuk, H. (1998), Existence of solutions for vector optimization problems, J. Math. Anal. Appl., Vol. 220, pp. 90–98.
Lee, G. M. and Kum, S. (1998), On implicit vector variational inequality, J. Optim. Theory Appl., (accepted).
Lin, K. L., Yang, D. P. and Yao, J. C. (1997), Generalized vector variational inequalities, J. Optim. Theory Appl., Vol. 92, pp. 117–125.
Park, S. (1992), Some coincidence theorems on acyclic multifunctions and applications to KKM theory, in Fixed point Theory and Applications, pp. 248–277.
Yang, X. Q. (1993), Generalized convex functions and vector variational inequalities, J. Optim. Theory Appl., Vol. 79, pp. 563–580.
Yang, X. Q. (1997), Vector variational inequality and multiobjective pseudolinear programming, J. Optim. Theory Appl., Vol. 95, pp. 729–734.
Yu, S. J. and Yao, J. C. (1996), On vector variational inequalities, J. Optim. Theory Appl., Vol. 89, pp. 749–746.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Kluwer Academic Publishers
About this chapter
Cite this chapter
Lee, G.M. (2000). On Relations between Vector Variational Inequality and Vector Optimization Problem. In: Yang, X., Mees, A.I., Fisher, M., Jennings, L. (eds) Progress in Optimization. Applied Optimization, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0301-5_12
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0301-5_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7986-7
Online ISBN: 978-1-4613-0301-5
eBook Packages: Springer Book Archive