A nonsmooth approach to envelope theorems

Olivier Morand, Kevin Reffett, Suchismita Tarafdar

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.

Original languageEnglish (US)
Pages (from-to)157-165
Number of pages9
JournalJournal of Mathematical Economics
Volume61
DOIs
StatePublished - Dec 1 2015

Fingerprint

Envelope
Non-convexity
Economics
Constraint Qualifications
Continuously differentiable
Equality Constraints
Constrained Optimization
Inequality Constraints
Nonlinear Optimization
Growth Model
Theorem
Value Function
Differentiable
Stochastic Model
Nonlinear Problem
Shock
Programming
Optimization Problem
Sufficient Conditions
Envelope theorem

Keywords

  • Constrained otimization with nonconvexities
  • Envelope theorems
  • Lattice programming
  • Nonsmooth analysis
  • Stochastic growth

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

Cite this

A nonsmooth approach to envelope theorems. / Morand, Olivier; Reffett, Kevin; Tarafdar, Suchismita.

In: Journal of Mathematical Economics, Vol. 61, 01.12.2015, p. 157-165.

Research output: Contribution to journalArticle

Morand, Olivier ; Reffett, Kevin ; Tarafdar, Suchismita. / A nonsmooth approach to envelope theorems. In: Journal of Mathematical Economics. 2015 ; Vol. 61. pp. 157-165.
@article{e5fa7566160540169823e4ddae2ab652,
title = "A nonsmooth approach to envelope theorems",
abstract = "We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.",
keywords = "Constrained otimization with nonconvexities, Envelope theorems, Lattice programming, Nonsmooth analysis, Stochastic growth",
author = "Olivier Morand and Kevin Reffett and Suchismita Tarafdar",
year = "2015",
month = "12",
day = "1",
doi = "10.1016/j.jmateco.2015.09.001",
language = "English (US)",
volume = "61",
pages = "157--165",
journal = "Journal of Mathematical Economics",
issn = "0304-4068",
publisher = "Elsevier",

}

TY - JOUR

T1 - A nonsmooth approach to envelope theorems

AU - Morand, Olivier

AU - Reffett, Kevin

AU - Tarafdar, Suchismita

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.

AB - We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian-Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.

KW - Constrained otimization with nonconvexities

KW - Envelope theorems

KW - Lattice programming

KW - Nonsmooth analysis

KW - Stochastic growth

UR - http://www.scopus.com/inward/record.url?scp=84948778042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948778042&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2015.09.001

DO - 10.1016/j.jmateco.2015.09.001

M3 - Article

AN - SCOPUS:84948778042

VL - 61

SP - 157

EP - 165

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -