Optimality and KKT conditions for interval valued optimization problems on Hadamard manifolds

Abstract

Recently, a new type of optimization problems, the so-called interval optimization problems on Hadamard manifolds, is introduced by the authors in Nguyen et al. [Interval optimization problems on Hadamard manifolds. J Nonlinear Convex Anal. 2023;24(11):2489–2511]. In this follow-up, we further offer the algorithmic bricks for these problems. More specifically, we characterize the optimality and KKT conditions for the interval valued optimization problems on Hadamard manifolds. For unconstrained problems, the existence of efficient points and the steepest descent algorithm are investigated. To the contrast, the KKT conditions and exact penalty approach are explored in the ones involving inequality constraints. These results pave the foundations for the solvability of interval valued optimization problems on Hadamard manifolds.