We consider two nonlinear programming problems with nonsmooth functions. The necessary and sufficient first order optimality conditions use the Dini and Clarke derivatives. However, the obtained Kuhn-Tucker conditions have a rather classical form. The sufficient conditions alone are obtained thanks to some properties of generalized convexity and generalized linearity of functions. The necessary and sufficient optimality conditions are given in the Lagrange form.
In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem.
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