Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1992-12-31
Sufficiency Conditions for Weak Local Minima in Multidimensional Optimal Control Problems with Mixed Control-State RestrictionsSabine Pickenhain (1) Brandenburgische Technische Universität Cottbus, Germany
In  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  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  for one-dimensional problems withoutstate restrictions.
Keywords: Sufficient optimality conditions, multidimensional control problems, parametric optimization
Pickenhain Sabine: Sufficiency Conditions for Weak Local Minima in Multidimensional Optimal Control Problems with Mixed Control-State Restrictions. Z. Anal. Anwend. 11 (1992), 559-568. doi: 10.4171/ZAA/584