Optimization in economies with nonconvexities
01 Jan 2010-
TL;DR: Conditions under which the Classical Lagrangian serves as an exact penalization of a nonconvex programming of a constrained optimization problems in economics are given.
Abstract: Nonconvex optimization is becoming the fashion to solve constrained optimization problems in economics. Classical Lagrangian does not necessarily represent a nonconvex optimization problem. In this paper, we give conditions under which the Classical Lagrangian serves as an exact penalization of a nonconvex programming. This has a simple interpretation and is easy to solve. We use this Classical Lagrangian to provide su¢ cient conditions under which value function is Clarke dif"
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134 citations
TL;DR: In this paper, 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 non-smooth objectives was developed.
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-Fromowitz 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.
13 citations
Cites background from "Optimization in economies with nonc..."
...Alternatively, one can also construct examples in which the SMFCQ fails, the MFCQ holds, and the value function is not C1 (see Tarafdar [24] for such examples, or an earlier draft of this paper....
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TL;DR: In this paper, 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 non-smooth objectives was developed.
10 citations
References
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TL;DR: In this article, lifetime aggregate labor supply with endogenous workweek length was studied and it was shown that policies designed to increase the length of the working life may not increase aggregate lifetime labor supply.
117 citations
"Optimization in economies with nonc..." refers background in this paper
..., Prescott, Rogerson, and Wallenius [49])....
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..., see Prescott, Rogerson, and Wallenius ([49]) and Rogerson and Wallenius ([55]))....
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115 citations
TL;DR: In this article, the authors examine how far the allocation of resources brought about by a perfectly competitive market remains optimal when indifference maps and production functions cease to be convex, and show that the traditional assumptions of convexity are by no means essential to the optimality of competitive markets.
Abstract: The object of this paper is to examine how far the allocation of resources brought about by s perfectly competitive market remains optimal when indifference maps and production functions cease to be convex. It has recently been asserted that the allocative efficiency of a competitive system breaks down under these circumstances. If this true, it would constitute s serious limitation, for, as I shall argue. In the real world the relevant functions are often not convex. However, we shall see that the traditional assumptions of convexity are by no means essential to the optimality of competitive markets and that the assertions to the contrary are based on an elementary fallacy. I shall examine in some detail the behavior of competitive markets under conditions of certainty.
110 citations
TL;DR: In this article, the authors developed several comparative dynamics results for multidimensional dynamic optimization problems in economics, and provided sufficient conditions for the value function to be monotone and supermodular.
100 citations
"Optimization in economies with nonc..." refers background in this paper
...In Amir [3], these ideas generalizes the nonclassical multisector models....
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TL;DR: In this article, a study of stability and differential stability in nonconvex programming with equality and inequality constraints is presented, where upper and lower bounds for the potential directional derivatives of the perturbation function (or the extremal value function) are obtained' with the help of a constraint qualification which is shown to be necessary and sufficient to have bounded multipliers.
Abstract: This paper consists of a study of stability and differential stability in nonconvex programming. For a program with equality and inequality constraints, upper and lower bounds are estimated for the potential directional derivatives of the perturbation function (or the extremal-value function). These results are obtained' with the help of a constraint qualification which is shown to be necessary and sufficient to have bounded multipliers. New results on the continuity of the perturbation function are also obtained.
99 citations