Strict Benson proper-ε-efficiency in vector optimization with set-valued maps

Authors

  • Kaur Surjeet Suneja University of Delhi, Department of Mathematics, Delhi, India
  • Megha Sharma_ University of Delhi, Department of Mathematics, Delhi, India

DOI:

https://doi.org/10.2298/YJOR131115007S

Keywords:

Ic-cone-convexlikeness, Set-valued Maps, Strict Benson proper-ε-efficiency, scalarization, ε-Lagrangian Multipliers

Abstract

In this paper the notion of Strict Benson proper-ε-efficient solution for a vector optimization problem with set-valued maps is introduced. The scalarization theorems and ε-Lagrangian multiplier theorems are established under the assumption of ic-cone-convexlikeness of set-valued maps.

References

Benson, H.P. (1979). An improved definition of proper efficiency for vector maximization with respect to cones. Journal of Mathematical Analysis and Applications, 71, 232-241.

Borwein, J.M. (1977). Proper efficient points for maximizations with respect to cones. SIAM Journal on Control and Optimization, 15, 57-63.

Chen, G.Y., & Huang, X.X. (1998). Ekeland’s variational principles for set-valued mappings. Mathematical Methods of Operations Research, 48, 181-186.

Chen, G.Y., & Rong, W.D. (1998). Characterization of the Benson proper efficiency for non convex vector optimization. Journal of Optimization Theory and Applications, 98, 365-384.

Cheng, Y.H., & Fu, W.T. (1999). Strong efficiency in a locally convex space. Mathematical Methods of Operations Research, 50, 373-384.

Geoffrion, A.M. (1968). Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications, 22, 618-630.

Jahn, J. (2004). Vector optimization theory, applications and extensions. Peter Lang, Springer-Verlag, Germany.

Kuhn, H.W., & Tucker, A.W. (1951). Nonlinear Programming. Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California, 481-492.

Li, Z.F. (1998). Benson Proper efficiency in vector optimization of set-valued maps. Journal of Optimization Theory and Applications, 98, 623-649.

Li, T., Xu, Y.H., & Zhu, C.X. (2007). -Strictly efficient solutions of vector optimization problems with set-valued maps. Asia Pacific Journal of Operational Research, 24(6), 841-854.

Liu, J.C. (1991). -Duality theorem of nondifferentiable multiobjective programming. Journal of Optimization Theory and Applications, 69, 153-167.

Rong, W.D., & Wu, Y.N. (2000). -Weak minimal solution of vector optimization problems with set-valued maps. Journal of Optimization Theory and Applications, 106(3), 569-579.

Sach, P.H. (2005). New generalized convexity notion for set-valued maps and application to vector optimization. Journal of Optimization Theory and Applications, 125, 157-179.

Downloads

Published

2015-10-01

Issue

Vol. 25 No. 3 (2015)

Section

Research Articles

License

Copyright (c) 2015 YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.