Parametrically Sufficient Optimality Conditions for Multiobjective Fractional Subset Programming Relating to Generalized $(\eta, \rho, \theta)$-Invexity of Higher Order

Authors

  • Ram U. Verma Department of Mathematics, Texas State University, San Marcos, Texas 78666

DOI:

https://doi.org/10.26713/jims.v5i3.221

Keywords:

Generalized invexity of higher order, Multiobjective fractional programming, Fractional subset programming, Sufficient optimality conditions

Abstract

Inspired by the recent investigations,  a general framework for a class of $(\eta, \rho,\theta)$-invex $n$-set functions of higher order $r\geq 1$ is introduced, and then some optimality conditions for multiobjective fractional programming on the generalized $(\eta,\rho,\theta)$-invexity are established. The obtained results are general in nature and unify various results on fractional subset programming in the literature.

Downloads

References

M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, {Journal of Mathematical Analysis and Applications} {80}(1981), 545-550.

L. Caiping and Y. Xinmin, Generalized $(rho,theta,eta)$-invariant monotonicity and generalized $(rho,theta, eta)$-invexity of non-differentiable functions, {Journal of Inequalities and Applications} Vol. {2009} (2009), Article ID # 393940, 16 pages.

H.C. Lai and T.Y. Huang, Minimax fractional programming for $n$-set functions and mixed-type duality under generalized invexity, {Journal of Optimization Theory and Applications} {bf 139} (2008), 295-313.

S.K. Mishra, M. Jaiswal and Pankaj, Optimality conditions for multiple objective fractional subset programming with invex an related non-convex functions, {Communications on Applied Nonlinear Analysis} {17}(3) (2010), 89-101.

S.K. Mishra, S.Y. Wang and K.K. Lai, Generalized convexity and vector optimization,

{Nonconvex Optimization and its Applications}, Vol. 19, Springer-Verlag, 2009.

R.U. Verma, Approximation solvability of a class of nonlinear set-valued inclusions involving $(A,eta)$-monotone mappings, {Journal of Mathematical Analysis and Applications} {337} (2008), 969-975.

R.U. Verma, The optimality condition for multiple objective fractional subset programming based on generalized $(rho,eta)$-invex functions, {Advances in Nonlinear Variational Inequalities} {14}(1) (2011), 61-72.

G.J. Zalmai and Q.B. Zhang, Generalized $(F,beta,phi,rho, theta)$-univex functions and parametric duality in semiinfinite discrete minmax fractional programming, {Advances in Nonlinear Variational Inequalities} {10}(2) (2007), 1-20.

G.J. Zalmai and Q.B. Zhang, Generalized $(F,beta,phi,rho, theta)$-univex functions and global parametric sufficient optimality conditions in semiinfinite discrete minmax fractional programming, {PanAmerican Mathematical Journal} {17}(3) (2007), 1-26.

Downloads

CITATION

How to Cite

Verma, R. U. (2013). Parametrically Sufficient Optimality Conditions for Multiobjective Fractional Subset Programming Relating to Generalized $(\eta, \rho, \theta)$-Invexity of Higher Order. Journal of Informatics and Mathematical Sciences, 5(3), 143–156. https://doi.org/10.26713/jims.v5i3.221

Issue

Vol. 5 No. 3 (2013)

Section

Research Article

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.