Advertisement

Semi-infinite Multiobjective Fractional Programming I

  • Ram U. VermaEmail author
Chapter
Part of the Infosys Science Foundation Series book series (ISFS)

Abstract

In this chapter, we first present three new classes of generalized convex functions involving Hadamard directional derivatives, namely, (strictly) (\(\mathcal {F},\) \(\beta ,\) \(\phi ,\) \(\rho ,\) \(\eta ,\) \(\theta ,\) \(\mu \))-Hd-univex functions, (strictly) (\(\mathcal {F},\) \(\beta ,\) \(\phi ,\) \(\rho ,\) \(\eta ,\) \(\theta ,\) \(\mu \))-Hd-pseudounivex functions, and (prestrictly) (\(\mathcal {F},\) \(\beta ,\) \(\phi ,\) \(\rho ,\) \(\eta ,\) \(\theta ,\) \(\mu \))-Hd-quasiunivex functions, and then, using these functions, we examine numerous sets of sufficient efficiency conditions for a semi-infinite multiobjective fractional programming problem with infinitely many equality and inequality constraints defined on a normed linear space. These results are crucial to further research endeavors.

References

  1. 1.
    Zalmai, G.J.: Semiinfinite multiobjective fractional programming problems involving Hadamard directionally differentiable functions, Part I : Sufficient efficiency conditions. Trans. Math. Prog. Appl. 1(9), 1–30 (2013)Google Scholar
  2. 2.
    Zalmai, G.J.: Semiinfinite multiobjective fractional programming problems involving Hadamard directionally differentiable functions, Part II : First-order parametric duality models. Trans. Math. Prog. Appl. 1(10), 1–34 (2013)Google Scholar
  3. 3.
    Zalmai, G.J.: Semiinfinite multiobjective fractional programming problems involving Hadamard directionally differentiable functions, Part III : First-order parameter-free duality models. Trans. Math. Prog. Appl. 2(1), 31–65 (2014)Google Scholar
  4. 4.
    Zalmai, G.J., Zhang, Q.: Global semiparametric sufficient efficiency conditions for semiinfinite multiobjective fractional programming problems involving generalized \((\alpha,\eta,\rho )\)-V-invex functions. Southeast Asian Bull. Math. 32, 573–599 (2008)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Zalmai, G.J., Zhang, Q.: Semiparametric duality models for semiinfinite multiobjective fractional programming problems involving generalized \((\alpha,\eta,\rho )\)-V-invex functions. Southeast Asian Bull. Math. 32, 779–804 (2008)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Zalmai, G.J., Zhang, Q.: Semiinfinite multiobjective fractional programming, part I : Sufficient efficiency conditions. J. Appl. Anal. 16, 199–224 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Zalmai, G.J., Zhang, Q.: Semiinfinite multiobjective fractional programming, part II : Parametric duality models. J. Appl. Anal. 17, 1–35 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Zalmai, G.J., Zhang, Q.: Global parametric sufficient efficiency conditions for semiinfinite multiobjective fractional programming problems containing generalized \((\alpha,\eta,\rho )\)-V-invex functions. Acta Math. Appl. Sinica 29, 63–78 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Zalmai, G.J., Zhang, Q.: Parametric duality models for semiinfinite multiobjective fractional programming problems containing generalized \((\alpha,\eta,\rho )\)-V-invex functions. Acta Math. Appl. Sinica 29, 225–240 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Zalmai, G.J., Zhang, Q.: Necessary efficiency conditions for semiinfinite multiobjective optimization problems involving Hadamard directionally differentiable functions. Trans. Math. Prog. Appl. 1, 129–147 (2013)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of MathematicsTexas State UniversitySan MarcosUSA

Personalised recommendations