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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title Envelope theorems for non-smooth and non-concave optimization
Organization Unit
  • Andrew Clausen
  • Carlo Strub
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 62
ISSN 1664-7041
Number of Pages 23
Date 2012
Abstract Text 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.
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Keywords Envelope theorem, differentiability, dynamic programming, discrete choice, nonsmooth analysis, diskrete Entscheidung, dynamische Optimierung, Variationsrechnung
Additional Information Revised version