On Duality with Support Functions for a Multiobjective Fractional Programming Problem

In this article, a different class of function called (K ×Q)-F-type I has been introduced. Further, we have formulated a problem over cones and appropriate duality results have been established taking the concerned functions to be(K×Q)F-type I. The results which we have put forward in the paper generalizes some of the known results appeared in the literature.

[1]  Sumit Kumar,et al.  Symmetric duality for a higher-order nondifferentiable multiobjective programming problem , 2015 .

[2]  R. Kaul,et al.  Optimality criteria and duality in multiple-objective optimization involving generalized invexity , 1994 .

[3]  M. A. Hanson On sufficiency of the Kuhn-Tucker conditions , 1981 .

[5]  Shashi Kant Mishra,et al.  Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions , 2014, Int. J. Math. Math. Sci..

[6]  Z. Jabeen,et al.  On fractional programming containing support functions , 2005 .

[7]  William S. Dorn A Duality Theorem for Convex Programs , 1960, IBM J. Res. Dev..

[8]  Xianfu Wang Subdifferentiability of real functions , 2005 .

[9]  Murray Schechter,et al.  More on subgradient duality , 1979 .

[10]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[11]  Izhar Ahmad,et al.  Unified higher order duality in nondifferentiable multiobjective programming involving cones , 2012, Math. Comput. Model..

[12]  S. K. Gupta,et al.  Duality for nondifferentiable multiobjective higher-order symmetric programs over cones involving generalized (F,α,ρ,d)-convexity , 2012 .

[13]  Surjeet Kaur Suneja,et al.  Higher order duality in multiobjective fractional programming with support functions , 2008 .

[14]  B. Craven Nonsmooth multiobjective programming , 1989 .

[15]  C. R. Bector,et al.  Optimality conditions and duality in subdifferentiable multiobjective fractional programming , 1993 .

[16]  Yu Jung Lee,et al.  Nondifferentiable higher order duality in multiobjective programming involving cones , 2009 .

[17]  Izhar Ahmad,et al.  Higher order symmetric duality in nondifferentiable multi-objective programming problems involving generalized cone convex functions , 2010, Math. Comput. Model..

[18]  M. A. Hanson,et al.  Necessary and sufficient conditions in constrained optimization , 1987, Math. Program..

[19]  T Tanino,et al.  Optimality and duality in nonsmooth multiobjective optimization involving generalized type I functions , 2003 .

[20]  M. A. Hanson,et al.  Optimality criteria in mathematical programming involving generalized invexity , 1988 .

[21]  Meetu Bhatia,et al.  Higher order duality in vector optimization over cones , 2012, Optim. Lett..