This paper addresses the optimization problems with interval-valued objective function. For this we consider two types of order relation on the interval space. For each order relation, we obtain KKT conditions using of the concept of generalized Hukuhara derivative (gH-derivative) for interval-valued functions. The gH-derivative is a concept more general of derivative for this class of functions than other concepts of derivative. We make some comparison with previous result given by other authors and we show some advantages of our result. © 2013 Springer Science+Business Media New York.