Skip to main content Accessibility help
×
Home

Unified duality for vector optimization problem over cones involving support functions

  • Surjeet Kaur Suneja (a1) and Pooja Louhan (a2)

Abstract

In this paper we give necessary and sufficient optimality conditions for a vector optimization problem over cones involving support functions in objective as well as constraints, using cone-convex and other related functions. We also associate a unified dual to the primal problem and establish weak, strong and converse duality results. A number of previously studied problems appear as special cases.

Copyright

References

Hide All
[1] Craven, B.D., Nonsmooth multiobjective programming. Numer. Func. Anal. Optim. 10 (1989) 4964.
[2] Mond, B. and Schechter, M., A duality theorem for a homogeneous fractional programming problem. J. Optim. Theory. Appl. 25 (1978) 349359.
[3] D.T. Luc, Theory of vector optimization. Springer (1989).
[4] Flores–Bazán, F. and Vera, C., Unifying efficiency and weak efficiency in generalized quasiconvex vector minimization on the real-line. Int. J. Optim. Theory: Theory, Methods and Appl. 1 (2009) 247265.
[5] Flores–Bazán, F., Hadjisavvas, N. and Vera, C., An optimal altenative theorem and applications to mathematical programming. J. Glob. Optim. 37 (2007) 229243.
[6] F.H. Clarke, Optimization and nonsmooth analysis. A Wiley-Interscience Publication (1983).
[7] Zalmai, G.J., Generalized (η,ρ)-invex functions and global semiparametric sufficient efficiency conditions for multiobjective fractional programming problems containing arbitrary norms. J. Glob. Optim. 36 (2006) 5185.
[8] Husain, I., Ahmed, A. and Mattoo, R.G., On multiobjective nonlinear programming with support functions. J. Appl. Anal. 16 (2010) 171187.
[9] Husain, I., Abha, and Jabeen, Z., On nonlinear programming with support functions. J. Appl. Math. Comput. 10 (2002) 8399.
[10] J. Jahn, Vector optimization: Theory, applications and extensions. Springer (2011).
[11] Schechter, M., A subgradient duality theorem. J. Math. Anal. Appl. 61 (1977) 850855.
[12] Schechter, M., More on subgradient duality. J. Math. Anal. Appl. 71 (1979) 251262.
[13] Cambini, R., Some new classes of generalized concave vector-valued functions. Optim. 36 (1996) 1124.
[14] R. Cambini and L. Carosi, Mixed type duality for multiobjective optimization problems with set constraints, in Optimality conditions in vector optimization, edited by Manuel Arana Jiménez, G. Ruiz-Garzón and A. Rufián-Lizan., Bentham Sci. Publishers, The Netherlands (2010) 119–142.
[15] Suneja, S.K., Louhan, P. and Grover, M.B., Higher-order cone-pseudoconvex, quasiconvex and other related functions in vector optimization. Optim. Lett. 7 (2013) 647664.
[16] Suneja, S.K., Sharma, S. and Vani, , Second-order duality in vector optimization over cones. J. Appl. Math. Inform. 26 (2008) 251261.
[17] Illés, T. and Kassay, G., Theorems of the alternative and optimality conditions for convexlike and general convexlike programming. J. Optim. Theory. Appl. 101 (1999) 243257.
[18] Weir, T., Mond, B. and Craven, B.D., Weak minimization and duality. Numer. Funct. Anal. Optim. 9 (1987) 181192.

Keywords

Unified duality for vector optimization problem over cones involving support functions

  • Surjeet Kaur Suneja (a1) and Pooja Louhan (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed