Roughly B-invex Multi-Objective Programming Problems

Abstract

In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.

Share and Cite:

T. Emam, "Roughly B-invex Multi-Objective Programming Problems," Open Journal of Optimization, Vol. 1 No. 1, 2012, pp. 1-7. doi: 10.4236/ojop.2012.11001.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] B. D. Craven, “Control and Optimization,” Chapman and Hall, London, 1995.
[2] H. X. Phu, “Six Kind of Roughly Convex Functions,” Journal of Optimization Theory and Applications, Vol. 92, No. 2, 1997, pp. 357-375. doi:10.1023/A:1022611314673
[3] S. K. Mishra, S. Y. Wang and K. K. Lai, “Generalized Convexity and Vector Optimization, Nonconvex Optimization and Its Applications,” Springer-Verlag, Berlin, 2009.
[4] S. K. Mishra and G. Giorgi, “Invexity and Optimization, Nonconvex Optimization and Its Applications,” SpringerVerlag, Berlin, 2008.
[5] S. K. Suneja, S. Khurana and Vani, “Generalized Nonsmooth Invexity over Cones in Vector Optimization,” European Journal of Operational Research, Vol. 186, No. 1, 2008, pp. 28-40. doi:10.1016/j.ejor.2007.01.047
[6] S. Komlosi, T. Rapesak and S. Schaible, “Generalized Convexity,” Springer-Verlag, Berlin, 1994.
[7] M. A. Hanson, “On Sufficiency of the Kuhn-Tucker Conditions,” Journal of Mathematical Analysis and Applications, Vol. 80, No. 2, 1981, pp. 545-550. doi:10.1016/0022-247X(81)90123-2
[8] C. R. Bector, S. K. Sunela and C. Singh, “Generalization of Preinvex and B-vex Functions,” Journal of Optimization Theory and Applications, Vol. 76, No. 3, 1993, pp. 277-287. doi:10.1007/BF00939383
[9] T. Emam, “Roughly B-invex Programming Problems,” Calcolo, Vol. 48, No. 2, 2011, pp. 173-188. doi:10.1007/s10092-010-0034-5
[10] T. Morsy, “A Study on Generalized Convex Mathematical Programming Problems, Master Thesis, Faculty of Science,” Suez Canal University, Egypt, 2003.
[11] V. Chankong and Y. Y. Haimes, “Multiobjective Decision Making Theory and Methodology,” North-Holland, Amsterdam, 1983.
[12] M. S. Bazaraa and C. M. Shetty, “Nonlinear Programming-Theory and Algorithms,” John Wiley and Sons, Inc., New York, 1979.
[13] T. Weir and B. Mond, “Generalized Convexity and Duality in Multiple Objective Programming,” Bulletin of the Australian Mathematical Society, Vol. 39, No. 2, 1989, pp. 287-299. doi:10.1017/S000497270000277X

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.