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Duality theory for state-contrained control problems governed by a first order PDE system. (English) Zbl 1126.49319
Summary: 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 $$y^\varepsilon$$ in the $$\varepsilon$$-maximum principle, proved by S. Pickenhain and M. Wagner [J. Optimization Theory Appl. 107, No. 2, 297–330 (2000; Zbl 0974.49011)], form a maximizing sequence in the dual problem.

##### MSC:
 49N15 Duality theory (optimization) 49K20 Optimality conditions for problems involving partial differential equations