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Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with ( G , α f )-Pseudobonvexity Assumptions

Author

Listed:
  • Ramu Dubey

    (Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, India)

  • Lakshmi Narayan Mishra

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, India)

  • Rifaqat Ali

    (Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia)

Abstract

In this paper, we introduce the various types of generalized invexities, i.e., α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex functions. Furthermore, we construct nontrivial numerical examples of ( G , α f ) -bonvexity/ ( G , α f ) -pseudobonvexity, which is neither α f -bonvex/ α f -pseudobonvex nor α f -invex/ α f -pseudoinvex with the same η . Further, we formulate a pair of second-order non-differentiable symmetric dual models and prove the duality relations under α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex assumptions. Finally, we construct a nontrivial numerical example justifying the weak duality result presented in the paper.

Suggested Citation

  • Ramu Dubey & Lakshmi Narayan Mishra & Rifaqat Ali, 2019. "Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with ( G , α f )-Pseudobonvexity Assumptions," Mathematics, MDPI, vol. 7(8), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:763-:d:259307
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