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Envelope theorems for non-smooth and non-concave optimization


Clausen, Andrew; Strub, Carlo (2012). Envelope theorems for non-smooth and non-concave optimization. Working paper series / Department of Economics 62, 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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C61, E20
Uncontrolled Keywords:Envelope theorem, differentiability, dynamic programming, discrete choice, nonsmooth analysis, diskrete Entscheidung, dynamische Optimierung, Variationsrechnung
Language:English
Date:April 2012
Deposited On:06 Jun 2018 12:38
Last Modified:27 Nov 2020 07:29
Series Name:Working paper series / Department of Economics
Number of Pages:23
ISSN:1664-7041
Additional Information:Revised version
OA Status:Green
Official URL:http://www.econ.uzh.ch/static/wp/econwp062.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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