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Existence Results and Finite Horizon Approximates for Infinite Horizon Optimization Problems
Sjur D. Flam
Roger J-B. J-B. Wets
Abstract
The paper deals with infinite horizon optimization problems. The existence of optimal solutions is obtained as a consequence of an asymptotic growth condition. We also construct finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long-term optimal trajectories. One type of approximate results from a process which involves smoothening the tail of any trajectory. The other type emerges when we restrain ourselves to stay put after a finite lapse of time.
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