Publication: Differentiability of the value function in continuous-time economic models
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2012-10
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Elsevier
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Abstract
In this paper we provide some sufficient conditions for the differentiability of the value
function in a class of infinite-horizon continuous-time models of convex optimization
arising in economics. We dispense with the assumption of interior optimal paths. This
assumption is quite unnatural in constrained optimization, and is usually hard to check
in applications. The differentiability of the value function is used to prove Bellman’s
equation as well as the existence and continuity of the optimal feedback policy. We also
establish the uniqueness of the vector of dual variables. These results become useful for
the characterization and computation of optimal solutions.
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Keywords
Constrained optimization, Value function, Differentiability, Envelope theorem, Duality theory
Bibliographic citation
Journal of mathematical analysis and applications, vol. 394, n. 1, Oct. 2012, pp. 305-323