Duality theory for optimization problems with interval-valued objective functions
To solve the investigated interval-valued nonlinear optimization problems a partial ordering of closed intervals is applied. Using this, a solution concept is suggested which is similar to the concept of a (weakly) nondominated solution in multicriterial optimization. To derive duality results, a Lagrange function is formulated which, for interval-valued optimization problems, is again interval-valued. Hence, the dual optimization problem is an interval-valued optimization problem, too. The weak duality result has then the form that, at feasible points, the dual objective function cannot dominate the primal one. Under convexity assumptions and if Slater's condition is satisfied it can be shown that there is no duality gap which means that the sets of optimal solutions of the primal and the dual problem intersect.
scientific article; zbMATH DE number 5696841