scholarly journals A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Takashi Kamihigashi
Keyword(s):  
Discrete Time ◽  
Infinite Horizon ◽  
Finite Measure ◽  
Infinite Horizon Optimization ◽  
Measure Spaces ◽  
Fatou’S Lemma ◽  
Fatou's Lemma

scholarly journals Optimality criteria for deterministic discrete-time infinite horizon optimization

2005 ◽  
Vol 2005 (1) ◽  
pp. 57-80 ◽  
Author(s):  
Irwin E. Schochetman ◽  
Robert L. Smith
Keyword(s):  
Discrete Time ◽  
Efficient Solution ◽  
Optimality Criterion ◽  
Infinite Horizon ◽  
Optimality Criteria ◽  
Efficient Solutions ◽  
Regularity Conditions ◽  
Sufficient Condition ◽  
Infinite Horizon Optimization ◽  
Continuous State

We consider the problem of selecting an optimality criterion, when total costs diverge, in deterministic infinite horizon optimization over discrete time. Our formulation allows for both discrete and continuous state and action spaces, as well as time-varying, that is, nonstationary, data. The task is to choose a criterion that is neither too overselective, so thatnopolicy is optimal, nor too underselective, so thatmostpolicies are optimal. We contrast and compare the following optimality criteria: strong, overtaking, weakly overtaking, efficient, and average. However, our focus is on the optimality criterion of efficiency. (A solution isefficientif it is optimal to each of the states through which it passes.) Under mild regularity conditions, we show that efficient solutions always exist and thus are not overselective. As to underselectivity, we provide weak state reachability conditions which assure that every efficient solution is also average optimal, thus providing a sufficient condition for average optima to exist. Our main result concerns the case where the discounted per-period costs converge to zero, while the discounted total costs diverge to infinity. Under the assumption that we can reach from any feasible state any feasible sequence of states in bounded time, we show that every efficient solution is also overtaking, thus providing a sufficient condition for overtaking optima to exist.

Efficiency in one-sector, discrete-time, infinite-horizon models

1984 ◽  
Vol 33 (1) ◽  
pp. 183-196 ◽  
Author(s):  
Anders Borglin ◽  
Hans Keiding
Keyword(s):  
Discrete Time ◽  
Infinite Horizon

scholarly journals Solvability in infinite horizon optimization

2015 ◽  
Vol 43 (5) ◽  
pp. 498-503 ◽  
Author(s):  
Timothy D. Lortz ◽  
Irina S. Dolinskaya ◽  
Archis Ghate ◽  
Robert L. Smith
Keyword(s):  
Infinite Horizon ◽  
Infinite Horizon Optimization
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