1 edition of Transversality conditions for some infinite horizon discrete time optimization problems found in the catalog.
Transversality conditions for some infinite horizon discrete time optimization problems
by Institute for Mathematical Studies in the Social Sciences, Stanford University in Stanford, Calif
Written in English
|Statement||by Ivar Ekeland and José Alexandre Scheinkman.|
|Series||Economics series / Institute for Mathematical Studies in the Social Sciences, Stanford University, Technical report / Institute for Mathematical Studies in the Social Sciences, Stanford University -- no. 411, Technical report (Stanford University. Institute for Mathematical Studies in the Social Sciences) -- no. 411., Economics series (Stanford University. Institute for Mathematical Studies in the Social Sciences)|
|Contributions||Scheinkman, José Alexandre.|
|The Physical Object|
|Pagination||27 p. :|
|Number of Pages||27|
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in both science and engineering. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the. Transversality conditions in infinite horizon models. [Washington, D.C.]: [Board of Governors of the Federal Reserve System?],  (OCoLC) Material Type: Government publication, National government publication, Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors.
"On the Transversality Condition in Infinite Horizon Optimal Problems." Econometr no. 4 (July ): Michel, Philippe. "Some Clarifications on the Transversality Condition." Econometr no. 3 (May ): Leung, Siu Fai. "Transversality Condition and Optimality in a Class of Infinite Horizon Continuous Time Economic. This video shows how to transform an infinite horizon optimization problem into a dynamic programming one. The Bellman equation or value function is calculated and then solved to obtain the Euler.
Dynamic Optimization Problems Deriving rst-order conditions: Certainty case We start with an optimizing problem for an economic agent who has to decide each period how to allocate his resources between consumption commodities, which provide instantaneous utility, and capital commodities, which provide production in the next period. (): "Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems," ~Mathernatics of Operations Research, 11, EWING,G. M. (): Calcul~ous of Variations with Applications.
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Abstract This paper considers a class of discrete-time, infinite-horizon optimization problems arising in economics. Necessary optimality conditions for such problems consist of an Euler equation and a transversality condition at infinity.
Our concern here is with the latter by: This paper considers a class of discrete-time, infinite-horizon optimization problems arising in economics. Necessary optimality conditions for such problems.
Kamihigashi [T. Kamihigashi, Necessity of transversality conditions for infinite horizon problems, Econometrica 69 () –] showed a generalization of their transversality condition that does not assume concavity. Using the variational approach, this paper deals with higher order differential problems: max x ∫ 0 ∞ v (x (t), xCited by: This gives rise to the general transversality conditions for the inﬂnite horizon problems: lim T!1 H (T)¢T = 0 and lim T!1 ‚(T)¢y(T) = 0: (12) Remark limT!1 H (T)¢T = 0 vanishes if the time horizon is assumed to be ﬂxed at 1.
Our general transversality condition is derived by directly following Chiang ()’s approach. Abstract. We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint by: There has been a large literature that considers the necessity and sufficiency of transversality conditions (TVCs) for infinite-horizon optimization problems with possibly unbounded objectives.
SOME CLARIFICATIONS ON THE TRANSVERSALITY CONDITION BY PHILIPPE MICHEL1 In this paper we study a general concave discrete time infinite horizon optimal control problem. We establish necessary and sufficient conditions for optimality in the weak sense the concave optimization problem is analyzed in Section 4, and the necessary.
TRANSVERSALITY CONDITIONS FOR SOME INFINITE HORIZON DISCRETE TIME OPTIMIZATION PROBLEMS*t IVAR EKELANDT AND JOSE ALEXANDRE SCHEINKMAN. This paper considers a class of discrete-time, infinite-horizon optimization problems arising in economics.
Necessary optimality conditions for such problems consist of an Euler equation. Models of Economics: The Continuous Time Case,” Journal of Economic The 1– Ekeland, I., and J.A. Scheinkman,“Transversality Conditions for Some Inﬁnite Hori-zon Discrete Time Optimization Problems,” Mathematics of Operations Resea – Transversality conditions are optimality conditions often used along with Eu-ler equations to characterize the optimal paths of dynamic economic models.
This article explains the foundations of transversality conditions using a ge-ometric example, a ﬁnite horizon problem, and an inﬁnite horizon problem. The Pontryagin Maximum Principle and Transversality Conditions for a Class of Optimal Control Problems with Infinite Time Horizons. This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons.
Ekeland I, Scheinkman JA: Transversality conditions for some infinite horizon discrete time optimization problems. Mathematics of Operations Research11(2) /moor MATH MathSciNet Article Google Scholar.
Downloadable (with restrictions). Abstract We obtain Euler–Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: Our results seem new and interesting even in the particular cases when the time scale is the set.
control theory for discrete-time problems on in nite horizon is far from being complete. A comprehensive account of the state of the art in the area, what concerns optimality conditions, is given in the recent book  by J.
Blot and N. Hayek. Ekeland and J. Scheinkman, Transversality conditions for some infinite horizon discrete time optimization problems, Math.
Oper. Res., 11 (), doi: /moor Google Scholar  S. Elaydi, "An Introduction to Difference Equations,", Third edition, (). Google Scholar . INFORMS Journal on Optimization; INFORMS Transactions on Education; Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems.
Ivar Ekeland, José Alexandre Scheinkman. Pages: Computational Complexity of Some Problems in Parametric Discrete Programming. Blair, R. Jeroslow. Pages: – where b(t) is some given function b: R +.
R +. Going to in–nite horizon the Maximum Principle still works, but we need to add some conditions at 1 (to replace the condition (T) = 0 we were using above). Su¢ ciency argument Let us go in reverse now and look –rst for su¢ cient conditions for an optimum. Transversality Conditions for Higher Order Infinite Horizon Discrete Time Optimization Problems.
In this paper, we examine higher order difference problems. Using the "squeezing" argument, we derive both Euler's condition and the transversality condition. In order to derive the two conditions, two needed assumptions are identified.
 G. Jumarie, An approach via fractional analysis to non-linearity induced by coarse-graining in space. Nonlinear Anal. Real World Appl. 11 ()  T. Kamihigashi, Necessity of transversality conditions for infinite horizon problems, Econo- metrica 69 () Applying this condition to a fairly general class of infinite-horizon deterministic optimization problems in discrete time, we establish a new result on the existence of an optimal path.
The condition takes a form similar to transversality conditions and other related conditions in dynamic optimization. NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION - Volume 20 Issue 3 - A. Kerem Coşar, Edward J. Green.This paper studies necessity of transversality conditions for the continuous time, reduced form model.
By generalizing Benveniste and Scheinkman's () “envelope” condition and Michel's () version of the squeezing argument, we show a generalization of Michel's (, Theorem 1) necessity result that does not assume concavity.This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons.
We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle. Special attention is paid to the behavior of the adjoint.