Abstract In this paper we study the optimal solutions set for a generalized differentiable interval-valued function. Necessary and sufficient optimality conditions are established for gH-differentiable functions. Convexity assumptions that are necessary or required to ensure the characterization of the optimal solutions are weaker or less strict than those presented in previous works. These convexity assumptions are the weakest to characterize the optimal solutions set. Known results for classical non interval-valued optimization are particular cases of the ones proved here.