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

Abstract

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 state-control restrictions. The result is obtained by applying duality theory for control problems of Klötzler \[11] as well as first and second order optimality conditions for optimization problems described by $C^$-functions having a locally Lipschitzian gradient mapping. The main theorem contains the result of Zeidan \[17] for one-dimensional problems withoutstate restrictions.