Abstract
In this paper, we consider a nondifferentiable convex vector optimization problem (VP), and formulate several kinds of vector variational inequalities with subdifferentials. Here we examine relations among solution sets of such vector variational inequalities and (VP).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Sawaragi H. Nakayama T. Tanino (1985) Theory of Multiobjective Optimization Academic Press New York, NY
F. Giannessi (1998) On Minty variational principle S. GiannessiF. Komlosi T. Rapcsák (Eds) New Trends in Mathematical Programming. Kluwer Academic Publishers Dordrecht Netherlands 93–99
G.M. Lee (2000) On relations between vector variational inequality and vector optimization problem X.Q. Yang A.I. Mees M.E. Fisher L.S. Jennings (Eds) Progress in Optimization. Kluwer Academic Publishers Dordrecht, Netherlands 167–179
G.M. Lee M.H. Kim (2001) ArticleTitleRemarks on relations between vector variational inequality and vector optimizaiton problem. Nonlienar Analysis: Theory, Methods and Applications 47 627–635
G.M. Lee M.H. Kim (2003) ArticleTitleOn second order necessary optimality conditions for vector optimization problems Journal of the Korean Mathematical Society 40 287–305
D.E. Ward G.M. Lee (2002) ArticleTitleOn relations between vector optimization problems and vector variational inequalities. Journal of Optimization Theory and Applications 113 583–596 Occurrence Handle10.1023/A:1015364905959
X.Q. Yang (1997) ArticleTitleVector variational inequality and multiobjective pseudolinear programming Journal of Optimization Theory and Applications 95 729–734 Occurrence Handle10.1023/A:1022694427027
A.M. Geoffrion (1968) ArticleTitleProper efficiency and the theory of vector maximization Journal of Mathematical Analysis Applications 22 618–630 Occurrence Handle10.1016/0022-247X(68)90201-1
H. Isermann (1974) ArticleTitleProper efficiency and the linear vector maximum problem Operations Research 22 189–191
J.P. Aubin (1979) Applied Functional Analysis John Wiley & Sons Inc. New York
O.L. Mangasarian (1969) Nonlinear Programming McGrow Hill New York
F.H. Clarke (1983) Optimization and Nonsmooth Analysis Wiley-Interscience New York.
G.M. Lee D.S. Kim B.S. Lee N.D. Yen (1998) ArticleTitleVector variational inequality as a tool for studying vector optimization problems Nonlinear Analysis: Theory, Methods and Applications 34 745–765
J. Jahn (1986) Mathematical Vector Optimization in Partially Ordered Linear Spaces Peter Lang Frankfurt am Main Germany
R.T. Rockafellar (1970) Convex Analysis Princeton University Press Princeton, New Jersey
J.-P. Vial (1983) ArticleTitleStrong and weak convexity of sets and functions Mathematical Operations Research 8 231–259
G.M. Lee N.D. Yen (2001) ArticleTitleA result on vector variational inequalities with polyhedral constraint sets Journal of Optimization Theory Applications 109 193–197 Occurrence Handle10.1023/A:1017522107088
N.D. Yen G.M. Lee (2000) On monotone and strongly monotone vector variational inequalities F. Giannessi (Eds) Vector Variational Inequalities and Vector Equilibria. Kluwer Academic Publishers Dordrecht, Netherlands 467–478
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject classification (2000). 90C25, 90C29, 65K10
This work was supported by the Brain Korea 21Project in 2003. The authors wish to express their appreciation to the anonymous referee for giving valuable comments.
Rights and permissions
About this article
Cite this article
Lee, G.M., Lee, K.B. Vector Variational Inequalities for Nondifferentiable Convex Vector Optimization Problems. J Glob Optim 32, 597–612 (2005). https://doi.org/10.1007/s10898-004-2696-5
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10898-004-2696-5