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Optimization in economies with nonconvexities
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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"read more
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Probability and measure, by Patrick Billingsley. Pp 515. £15·20. 1979. SBN 0 471 03173 9 (Wiley)
Journal ArticleDOI
A Nonsmooth Approach to Envelope Theorems
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.
Journal ArticleDOI
A nonsmooth approach to envelope theorems
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.
References
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Book
Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications)
Diethard Klatte,Bernd Kummer +1 more
TL;DR: In this article, a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions, is presented, along with an analysis of generalized Newton methods based on linear and nonlinear approximations.
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Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics
TL;DR: In this paper, the authors study a model of lumpy investment wherein establishments face persistent shocks to common and plant-specific productivity, and nonconvex adjustment costs lead them to pursue generalized (S,s) investment rules.
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Strict Monotonicity in Comparative Statics
TL;DR: In this article, the authors extend the lattice-theoretic results of Milgrom and Shannon by imposing a stronger differential version of the single crossing property and arguing from first-order conditions.
Posted Content
Are Nonconvexities Important for Understanding Growth
TL;DR: This article argued that nonconvexity is essential for economic growth and pointed out the difference between public goods and the technological advances that are fundamental to economic growth, emphasizing the distinction between two of the fundamental attributes of any economic good: rivalry and excludability.
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Bargaining in a network of buyers and sellers
TL;DR: Graph theory tools are used to provide necessary and sufficient conditions regarding the architecture of networks for the subgame perfect equilibrium of the bargaining game to coincide with the Walrasian outcome.