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Optimization in economies with nonconvexities
TLDR
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
Citations
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Journal ArticleDOI
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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Journal ArticleDOI
Envelope Theorems for Arbitrary Choice Sets
Paul Milgrom,Ilya Segal +1 more
TL;DR: The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative as mentioned in this paper.
Journal ArticleDOI
The Existence of Equilibrium in Discontinuous Economic Games, I: Theory
Eric Maskin,Partha Dasgupta +1 more
TL;DR: In this article, the existence of Nash equilibrium in games where agents' payoff functions are discontinuous is investigated, and it is shown that the payoff functions in mildly modified versions of these constructs exhibit two weaker forms of continuity which, together with the requirement of quasi-concavity, suffice for the presence of an equilibrium.
Book
Implicit Functions and Solution Mappings
TL;DR: In this article, the authors provide a reference on the topic and a unified collection of a number of results which are currently scattered throughout the literature, including implicit mappings defined by relations other than equations.
Journal ArticleDOI
On the differentiability of the value function in dynamic models of economics
Book
Cost curves and supply curves ..
TL;DR: In this article, the authors present a graphical exposition of the manner in which supply curves are dependent upon the different possible types of technological and pecuniary cost situations, under the usual assumptions of atomistic competition and of rational economic behavior on the part of the producers.