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Unified duality for vector optimization problem over conesinvolving support functions

Published online by Cambridge University Press:  21 March 2014

Surjeet Kaur Suneja  and
Pooja Louhan
Surjeet Kaur Suneja
Affiliation:
Department of Mathematics, Miranda House, University of Delhi, Delhi-110 007, India.. [email protected]
Pooja Louhan
Affiliation:
Department of Mathematics, University of Delhi, Delhi-110 007, India.; [email protected].
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Abstract

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

Keywords

Vector optimizationconessupport functionoptimalityduality
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 3 , July 2014 , pp. 271 - 302
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

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References

Craven, B.D., Nonsmooth multiobjective programming. Numer. Func. Anal. Optim. 10 (1989) 49–64. Google Scholar
Mond, B. and Schechter, M., A duality theorem for a homogeneous fractional programming problem. J. Optim. Theory. Appl. 25 (1978) 349–359. Google Scholar
D.T. Luc, Theory of vector optimization. Springer (1989).
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) 247–265. Google Scholar
Flores–Bazán, F., Hadjisavvas, N. and Vera, C., An optimal altenative theorem and applications to mathematical programming. J. Glob. Optim. 37 (2007) 229–243. Google Scholar
F.H. Clarke, Optimization and nonsmooth analysis. A Wiley-Interscience Publication (1983).
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) 51–85. Google Scholar
Husain, I., Ahmed, A. and Mattoo, R.G., On multiobjective nonlinear programming with support functions. J. Appl. Anal. 16 (2010) 171–187. Google Scholar
Husain, I., Abha, and Jabeen, Z., On nonlinear programming with support functions. J. Appl. Math. Comput. 10 (2002) 83–99. Google Scholar
J. Jahn, Vector optimization: Theory, applications and extensions. Springer (2011).
Schechter, M., A subgradient duality theorem. J. Math. Anal. Appl. 61 (1977) 850–855. Google Scholar
Schechter, M., More on subgradient duality. J. Math. Anal. Appl. 71 (1979) 251–262. Google Scholar
Cambini, R., Some new classes of generalized concave vector-valued functions. Optim. 36 (1996) 11–24. Google Scholar
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.
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) 647–664. Google Scholar
Suneja, S.K., Sharma, S. and Vani, , Second-order duality in vector optimization over cones. J. Appl. Math. Inform. 26 (2008) 251–261. Google Scholar
Illés, T. and Kassay, G., Theorems of the alternative and optimality conditions for convexlike and general convexlike programming. J. Optim. Theory. Appl. 101 (1999) 243–257. Google Scholar
Weir, T., Mond, B. and Craven, B.D., Weak minimization and duality. Numer. Funct. Anal. Optim. 9 (1987) 181–192. Google Scholar