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

  • Sabine Pickenhain

    Brandenburgische Technische Universität Cottbus, Germany

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 -functions having a locally Lipschitzian gradient mapping. The main theorem contains the result of Zeidan [17] for one-dimensional problems withoutstate restrictions.

Cite this article

Sabine Pickenhain, Sufficiency Conditions for Weak Local Minima in Multidimensional Optimal Control Problems with Mixed Control-State Restrictions. Z. Anal. Anwend. 11 (1992), no. 4, pp. 559–568

DOI 10.4171/ZAA/584