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In [13] a new sufficiency criterion for strong local minimality in multidimensional non-convex control problems with pure state constraint was developed. In this paper we use a similar method to obtain sufficient conditions for weak local minimality in multidimensional control problems with mixed statecontrol restrictions. The result is obtained by applying duality theory for control problems of KLOTzLER [11] as well as first and second order optimality conditions for optimization problems described by C 1 functions having a locally Lipschitzian gradient mapping. The main theorem contains the result of ZEIDAN [17] for one-dimensional problems withoutstate restrictions.

Sufficiency Conditions for Weak Local Minima in Multidimensional Optimal Control Problems with Mixed Control-State Restrictions