A nonsmooth approach to envelope theorems

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• 作者：Olivier Morand^a ; Kevin Reffett^b ; Suchismita Tarafdar^c ; ^{suchismita.tarafdar@snu.edu.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Constrained otimization with nonconvexities ; Envelope theorems ; Nonsmooth analysis ; Stochastic growth ; Lattice programming
• 刊名：Journal of Mathematical Economics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：61
• 期：Complete
• 页码：157-165
• 全文大小：431 K

文摘

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.