2015
DOI: 10.1016/j.ejor.2014.08.003
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Approximate dynamic programming for stochastic linear control problems on compact state spaces

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Cited by 10 publications
(4 citation statements)
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“…Calculations obtained with the help of the algorithm from subsection 2.3. 9. r 5 10. r 10 11. r 16 12. r 6 13. r 15 14. r 9 15. r 4 16. r 12…”
Section: E Compromise Hypersphere Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Calculations obtained with the help of the algorithm from subsection 2.3. 9. r 5 10. r 10 11. r 16 12. r 6 13. r 15 14. r 9 15. r 4 16. r 12…”
Section: E Compromise Hypersphere Methodsmentioning
confidence: 99%
“…Sitarz [4] shows a usage of dynamic programming into multiple knapsack problem. In [5] the stochastic dynamic programming on compact state spaces is discussed. Whereas the idea of compromise hypersphere comes from the work by Gass and Roy [6].…”
Section: Introductionmentioning
confidence: 99%
“…However, state space, action space and external information space grow as the size of the problem is getting larger, causing the curse of dimensionality. Approximate dynamic programming [17] take advantages of the optimal control theory, approximation techniques and reinforcement learning theory, mainly aiming at solving dimensionality curse problems. The main idea of approximate dynamic programming is to use approximate method to predict and control the state of the approximate value function by Monte Carlo [18] simulation and statistical methods to sample states and external information…”
Section: Approximate Dynamic Programmingmentioning
confidence: 99%
“…Beyond Chow, there are of course many other important contributions to the topic of stochastic optimal control in continuous time, many of these use duality, for example Ma et al (2020), and it would be very interesting to connect the Lagrange formalism explored in our paper to these. Further, Wörner et al (2015) propose an approximate relative value iteration algorithm based on piecewise-linear convex relative value function approximations, which would be interesting to investigate from the perspective of the Lagrange multiplier theorem and our proposed numerical scheme in section 4, which is partly Monte Carlo based. We leave both of these avenues for future research.…”
Section: Introductionmentioning
confidence: 99%