The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
"Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems." J. Appl. Math. 2013 (SI07) 1 - 11, 2013. https://doi.org/10.1155/2013/641345