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Optimization in economies with nonconvexities
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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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On optimal growth under uncertainty
TL;DR: In this paper, necessary and sufficient conditions for optimal policy functions are derived in a regime in which future utilities are discounted, leading to an explicit optimal policy function, which is used to display the steady-state solution for the capital stock under an optimal policy.
BookDOI
Lagrange-type functions in constrained non-convex optimization
TL;DR: The question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimization problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints.
Journal ArticleDOI
Probability and measure, by Patrick Billingsley. Pp 515. £15·20. 1979. SBN 0 471 03173 9 (Wiley)
Journal ArticleDOI
The Comparative Statics of Constrained Optimization Problems
TL;DR: In this article, the problem of maximizing a real-valued function when the objective function is constrained to lie in some subset of R l is studied, and a natural way to order the constraint sets C and find the corresponding restrictions on the objective functions that guarantee that optimal solutions increase with the constraint set is developed.
Journal ArticleDOI
On uniqueness of Kuhn-Tucker multipliers in nonlinear programming
TL;DR: It is shown that this new constraint qualification is a necessary and sufficient condition for the uniqueness of Kuhn—Tucker multipliers and implies the satisfaction of second order necessary optimality conditions at a local minimum.