Multiobjective Dynamic Optimization of Cooperative Difference Games in Infinite Horizon

2020 ◽  
pp. 1-12 ◽  
Author(s):  
Chenchen Peng ◽  
Weihai Zhang
Keyword(s):  
Dynamic Optimization ◽  
Infinite Horizon

scholarly journals A CORRESPONDENCE-THEORETIC APPROACH TO DYNAMIC OPTIMIZATION

2009 ◽  
Vol 13 (S1) ◽  
pp. 97-117 ◽  
Author(s):  
C. D. Aliprantis ◽  
G. Camera
Keyword(s):  
Fixed Point ◽  
Dynamic Optimization ◽  
Fixed Point Theorems ◽  
Infinite Horizon ◽  
Economic Models ◽  
Theoretic Approach ◽  
Transversality Conditions ◽  
Recursive Formulation ◽  
Bellman Equations ◽  
The Common

This paper introduces a method of optimization in infinite-horizon economies based on the theory of correspondences. The proposed approach allow us to study time-separable and non-time-separable dynamic economic models without resorting to fixed point theorems or transversality conditions. When our technique is applied to the standard time-separable model it provides an alternative and straightforward way to derive the common recursive formulation of these models by means of Bellman equations.

scholarly journals A contraction approach to dynamic optimization problems

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0260257
Author(s):  
Leif K. Sandal ◽  
Sturla F. Kvamsdal ◽  
José M. Maroto ◽  
Manuel Morán
Keyword(s):  
Dynamic Optimization ◽  
General Class ◽  
Dynamic Games ◽  
Optimization Problems ◽  
Infinite Horizon ◽  
Management Problem ◽  
Coupled Equations ◽  
Special Cases ◽  
Rigorous Treatment ◽  
Special Case

An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions. Solutions are obtained by considering a vector-valued value function and by using an iterative process. Special cases of the general class of contraction problems include the classical Bellman problem and its stochastic formulations. Thus, our approach can be viewed as an extension of the Bellman problem to the special case of nonautonomy that periodicity represents, and our approach thereby facilitates consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization, and furthermore, certain types of dynamic games. The contraction approach is illustrated in simple examples. In the main example, which is an infinite-horizon resource management problem with a periodic price, it is found that the optimal exploitation level differs between high and low price time intervals and that the solution time paths approach a limit cycle.

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