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

• DOI: 10.48550/arxiv.2309.09396
• Publication Date: 2023-01-01
• Authors: Hilal Ahmad Bhat; Akhlad Iqbal; Mahwash Aftab
• Keywords: Karush–Kuhn–Tucker conditions

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 optimization problem Based type involved in problems, we consider the following cases: 1. objective function as well constraints are real-valued; 2. is and 3. contraints interval-valued. whole theory justified with help examples. order relation that use throughout paper a complete collection all closed bounded intervals $\mathbb{R}$.