Interval valued optimization problems on Hadamard manifolds

Abstract

NoneIn this thesis, we study the interval valued optimization problems (IOPs)on Hadamard manifolds, including unconstrained and constrained problems. Toachieve the theoretical results, we build up some new concepts about gH-directional derivative, gH-Gâteaux and gH-Fréchet differentiability of interval valued functions with their properties on Hadamard manifolds. More specifically, we characterize the optimality conditions for the IOPs on the Hadamard manifolds. For unconstrained problems, the existence of efficient points and the steepest descent algorithm are investigated. To the contrast, the optimality conditions, exact penalty, and duality approach are explored in the ones involving inequality constraints. The obtained results pave a way to further study on Riemannian interval optimization problems (RIOPs).