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arXiv · 2309.09396

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

Hilal Ahmad Bhat·Akhlad Iqbal·Mahwash Aftab
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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 type of functions involved in optimization problems, we consider the following cases: 1. objective function as well as constraints are real-valued; 2. objective function is interval-valued, and constraints are real-valued; 3. 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 $\mathbb{R}$.

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Hilal Ahmad Bhat, Akhlad Iqbal, Mahwash Aftab. 2023-09-17. Optimality Conditions for Interval-Valued Optimization Problems on Riemannian Manifolds Under a Total Order Relation. https://doi.org/10.1007/s10957-025-02618-3

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