On interval-valued nonlinear programming problems

The Wolfe's duality theorems in interval-valued optimization problems are derived in this paper. Four kinds of interval-valued optimization problems are formulated. The Karush–Kuhn–Tucker optimality conditions for interval-valued optimization problems are derived for the purpose of proving the strong duality theorems. The concept of having no duality gap in weak and strong sense are also introduced, and the strong duality theorems in weak and strong sense are then derived naturally.