Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines

This paper presents an extended Karush-Kuhn-Tucker condition to characterize efficient solutions to constrained interval optimization problems. We develop the theory from the geometrical fact that at an optimal solution the cone of feasible directions and the set of descent directions have an empty intersection. With the help of this fact, we derive a set of first-order optimality conditions for unconstrained interval optimization problems. In...