Summary.
This note offers a new proof of the necessary conditions for fixed endpoint optimal control. Our approach simplifies the conventional derivation of the necessary conditions by using a transversality condition to ensure feasibility of modifications to the optimal path. We further prove that this transversality condition holds automatically at the optimum and can therefore be ignored in the statement of the necessary conditions.
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Received: 23 February 2004, Revised: 22 November 2004,
JEL Classification Numbers:
C61.
Correspondence to: Frank Caliendo
We thank Ken Lyon for many stimulating discussion on optimal control theory, and an anonymous referee for helpful feedback. We are also grateful for the careful treatment of fixed endpoint problems in Kamien and Schwartz (1991, pp. 147-153), which has served as a guide and point of reference for our work.
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Caliendo, F., Pande, S. Fixed endpoint optimal control. Economic Theory 26, 1007–1012 (2005). https://doi.org/10.1007/s00199-004-0589-y
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DOI: https://doi.org/10.1007/s00199-004-0589-y