Necessary and sufficient conditions for calculus of variations under interval uncertainty

摘要

In this paper, a complete investigation of necessary and sufficient conditions is discussed on the variational problems under interval uncertainty. More precisely, it is shown that based on the parametric representation of an interval, the interval variational problems can be interpreted as a set of classical variational problems. Finally, to show the ability and significance of this point of view on the necessary and sufficient conditions, two comprehensive examples are proposed, more specifically the Hanging Cable Problem.