A nonsmooth approach to envelope theorems |
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| Affiliation: | 1. Department of Economics, University of Connecticut, United States;2. Department of Economics, WP Carey School of Business, Arizona State University, United States;3. Department of Economics, Shiv Nadar University, India;1. Department of Economics, University of Iowa, Iowa City, USA;2. Department of Economics, Michigan State University, East Lansing, USA;3. Department of Economics, University of Arizona, Tucson, USA;1. Dipartimento di Matematica e Informatica, University of Cagliari, Italy;2. Dipartimento di Scienze Economiche e Aziendali, University of Cagliari, viale S. Ignazio 17, 09123 Cagliari, Italy;1. Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, the Netherlands;2. Research School of Economics, Australian National University, Canberra, Australia |
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| 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. |
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| Keywords: | Constrained otimization with nonconvexities Envelope theorems Nonsmooth analysis Stochastic growth Lattice programming |
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