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This work is concerned with mathematical programming problems with inequality constraints in which the objective function is interval-valued. Necessary optimality conditions of Karush-Kuhn-Tucker type are derived through a geometric approach and the use of the generalized Hukuhara differentiability concept.

In this work, it will be considered optimal control problems in which the objective function is interval-valued. The concept of optimality will be defined through the lower-upper order relation (LU-order). Problem data is assumed to satisfy merely Lipschitz continuity. Necessary optimality conditions in the form of a maximum principle are obtained.

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