Optimality conditions for interval valued optimization problems

This work addresses constrained optimization problems in which the objective function is interval-valued while the inequality constraints functions are real-valued. Both necessary and sufficient optimality conditions are derived. They are given through the gH-gradient and the gH-directional derivative of the interval objective function. The necessary ones are of KKT-type. The sufficient conditions are of generalized convexity type. The developed theory is illustrated by means of some numerical examples.