## Distributed Dynamic Programming (1982)

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Citations: | 509 - 24 self |

### Citations

325 |
Combinatorial Optimization: Networks and
- Lawler
- 1976
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Citation Context ...i,j) is a link. Assume that each link (i,j) is assigned a positive scalar a.. referred to as its length. Assume also13 that there is a directed path to node 1 from every other node. Then it is known (=-=[4]-=-, p. 67) that the shortest path distances d to node 1 from 1 all other nodes i solve uniquely the equations d* = min {a.. + d}, Vi 1 (6a) 1 jsN(i)sd* = 0. (6b) If we make the identifications S = C - N... |

222 |
Dynamic Programming and Stochastic Control
- Bertsekas
- 1976
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Citation Context ...niformly bounded above and below by some scalars and 0 < a 1 the- problem is equivalent to the standard infinite horizon discounted stochastic optimal control problem with bounded cost per stage (see =-=[5]-=- Sections 6.1-6.3). Under these circumstances the mapping T of (4) has a unique fixed point J* in the class of all bounded real valued functions on S and J* is the optimal value function of the corres... |

133 |
Stochastic Optimal Control: The Discrete-Time Case. Athena Scientific
- Bertsekas, Shreve
- 1996
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Citation Context ...ledge there is no published proof of convergence of this algorithm. _1__ ___s 1_1 _ - %? -,fi -42. Problem Formulation We use an abstract framework of dynamic programming, first introduced in [2], =-=[3]-=- which includes as special cases a number of specific problems of practical interest. Let S and C be two sets referred to as the state space and the control space respectively. Elements of S and C are... |

46 |
A review of the development and performance of the ARPANET routing algorithm
- McQuillan, Galk, et al.
- 1978
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Citation Context ...These include-shortest .--- path problems for which the distributed algorithm of this paper turns out to be essentially the same as the routing algorithm originally implemented in the ARPANET in 1969 =-=[1]-=-. To our knowledge there is no published proof of convergence of this algorithm. _1__ ___s 1_1 _ - %? -,fi -42. Problem Formulation We use an abstract framework of dynamic programming, first introd... |

24 |
Dynamic Programming, Markov Chains, and the Method of Successive Approximations
- White
- 1963
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Citation Context ...an decision problems involving a finite state space and minimization of average cost per stage (Howard [6]), a distributed asynchronous version of the usual dynamic programming algorithm due to White =-=[7]-=- (see [5], Section 8.2) may fail to converge to the correct solution. This is illustrated in the following example constructed by John Tsitsiklis. In this example the basic mapping H does not satisfy ... |

17 |
Monotone Mappings with Application in Dynamic Programming
- Bertsekas
- 1977
(Show Context)
Citation Context ... knowledge there is no published proof of convergence of this algorithm. _1__ ___s 1_1 _ - %? -,fi -42. Problem Formulation We use an abstract framework of dynamic programming, first introduced in =-=[2]-=-, [3] which includes as special cases a number of specific problems of practical interest. Let S and C be two sets referred to as the state space and the control space respectively. Elements of S and ... |

12 | electrical engineering from - in - 1984 |

1 | Monotone mappings Kith application in dynamic programming." S1.4 .tf 1 - Bcrtaekas - 1977 |

1 | Opri~~ul Control: The Drsc.rerr-7rnre Cuse - hasric - 1978 |

1 | Drrlumic Progrutmrrrrtg ami Srarhartic Cotmol - Bertsekas - 1976 |

1 | Bertsekas (S'70-SM77) received the Diploma of Mechanical and Electrical Engineering from the National - Dimitri - 1965 |

1 | ssn.ed on th2 faculty of Stanford Universit>- and the University of Illinois. He is currently Professor of Electrical Engineering and Computer Science at M.I.T. His research interest5 are in optimization theoy and algorithmic aspects of communication netw - has - 1978 |

1 |
Dynamic Programming and Markoy Prceases
- Howard
- 1960
(Show Context)
Citation Context ...sential for the validity of the result described above. Indeed for the important class of Markovian decision problems involving a finite state space and minimization of average cost per stage (Howard =-=[6]-=-), a distributed asynchronous version of the usual dynamic programming algorithm due to White [7] (see [5], Section 8.2) may fail to converge to the correct solution. This is illustrated in the follow... |