Envelope theorems for non-smooth and non-concave optimization

Andrew Clausen and Carlo Strub ()

No 62, ECON - Working Papers from Department of Economics - University of Zurich

Abstract: We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem: first-order conditions are necessary at interior optimal choices. We only assume differentiability of the utility function with respect to the continuous choices. The continuous choice may be from any Banach space and the discrete choice from any non-empty set.

Keywords: Envelope theorem; differentiability; dynamic programming; discrete choice; non-smooth analysis (search for similar items in EconPapers)
JEL-codes: C61 E20 (search for similar items in EconPapers)
Date: 2012-04
New Economics Papers: this item is included in nep-dcm, nep-mic and nep-upt
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Citations: View citations in EconPapers (17)

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Working Paper: A General and Intuitive Envelope Theorem (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:zur:econwp:062

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