A solution concept in optimization problems with interval-valued objective functions, which is essentially similar to the concept of nondominated solution in multiobjective programming problems, is introduced by imposing a partial ordering on the set of all closed intervals. The interval-valued Lagrangian function and interval-valued Lagrangian dual function are also proposed to formulate the dual problem. Under these settings, the weak and strong duality theorems can be elicited. We show that there is no duality gap between the primal and dual problems under suitable assumptions for interval-valued functions.
Journal of Optimization Theory and Applications / vol.144, P. 615-628