A nonsmooth approach to envelope theorems

Olivier Morand, Kevin Reffett, Suchismita Tarafdar

Research output: Contribution to journalArticle

4 Scopus citations

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

Keywords

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

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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