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A nonsmooth approach to envelope theorems

Olivier Morand, Kevin Reffett and Suchismita Tarafdar

Journal of Mathematical Economics, 2015, vol. 61, issue C, 157-165

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; Nonsmooth analysis; Stochastic growth; Lattice programming (search for similar items in EconPapers)
Date: 2015
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Handle: RePEc:eee:mateco:v:61:y:2015:i:c:p:157-165