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The Pontryagin Maximum Principle is a necessary condition of optimality for infinite horizon control problems, however for these problems it can be degenerate. We announce that the Lipschitz continuity of the value function implies the normal form version of the Pontryagin Maximum Principle, moreover normal co-state arc becomes a gradient of value function.


control problem; infinite horizon problem; necessary conditions of optimality; Pontryagin maximum principle; value function; shadow price; limiting gradient

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