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Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation

Author

Listed:
  • Hilal Ahmad Bhat

    (Aligarh Muslim University)

  • Akhlad Iqbal

    (Aligarh Muslim University)

  • Mahwash Aftab

    (Aligarh Muslim University)

Abstract

This article explores fundamental properties of convex interval-valued functions defined on Riemannian manifolds. The study employs generalized Hukuhara directional differentiability to derive KKT-type optimality conditions for an interval-valued optimization problem on Riemannian manifolds. Based on the type of functions involved in optimization problems, we consider the following cases: objective function as well as constraints are real-valued; objective function is interval-valued and constraints are real-valued; objective function as well as constraints are interval-valued. The whole theory is justified with the help of examples. The order relation that we use throughout the paper is a total order relation defined on the collection of all closed and bounded intervals in $$\mathbb {R}$$ R .

Suggested Citation

  • Hilal Ahmad Bhat & Akhlad Iqbal & Mahwash Aftab, 2025. "Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-29, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02618-3
    DOI: 10.1007/s10957-025-02618-3
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    References listed on IDEAS

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