Abstract
This paper presents local optimality and stability conditions for stationary solutions of autonomous optimal control problems with a positive rate of discounting. The conditions do not require the Hamiltonian function to be concave with respect to the state variables. Two examples from optimal economic growth theory are discussed to show that our results can be applied in situations when other known stability conditions fail to be satisfied.
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Communicated by G. Leitmann
Part of this paper was written while the author visited the Faculty of Management at the University of Toronto. Support from SSHRC Grant 410-83-9888 and from Grant P6601 of the Austrian Science Foundation is gratefully acknowledged.
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Sorger, G. Local stability of stationary states in discounted optimal control systems. J Optim Theory Appl 72, 143–162 (1992). https://doi.org/10.1007/BF00939953
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DOI: https://doi.org/10.1007/BF00939953