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Zeitschrift für Analysis und ihre Anwendungen


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Volume 11, Issue 4, 1992, pp. 559–568
DOI: 10.4171/ZAA/584

Published online: 1992-12-31

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

Sabine Pickenhain[1]

(1) Brandenburgische Technische Universität Cottbus, Germany

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.

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