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In this paper we summarize our results in infinite horizon optimal control.We present optimality conditions for weak local minimizer in the framework ofweighted functions. Moreover we formulate the Pontryagin Maximum Principle forstrong local minimizer for trajectories converging at infinity. The consideredproblems, the requirements and the results depend on the choice of the functionspace.

Optimality Conditions for Weak and Strong Local Extrema in Infinite Horizon Optimal Control Problems