## Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time (1990)

Venue: | SIAM J. Control Opt |

Citations: | 32 - 7 self |

### BibTeX

@ARTICLE{Rockafellar90generalizedlinear-quadratic,

author = {R. T. Rockafellar and R. J-b. Wets},

title = {Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time},

journal = {SIAM J. Control Opt},

year = {1990},

pages = {810--822}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Two fundamental classes of problems in large-scale linear and quadratic programming are described. Multistage problems covering a wide variety of models in dynamic programming and stochastic programming are represented in a new way. Strong properties of duality are revealed which support the development of iterative approximate techniques of solution in terms of saddlepoints. Optimality conditions are derived in a form that emphasizes the possibilities of decomposition.

### Citations

3267 | Convex Analysis - Rockafellar - 1970 |

166 |
An algorithm for quadratic programming
- Frank, Wolfe
- 1956
(Show Context)
Citation Context ...lationship between (P) and (Q) can be derived from the standard theory of linear and quadratic programming, specifically the duality theorem of Cottle [6] and the existence theorem of Frank and Wolfe =-=[7]-=-. Theorem 2.1 (Rockafellar and Wets [3, Theorem 2]). If either (P) or (Q) has finite optimal value, or if both problems have feasible solutions, then both optimal values are finite and equal, and both... |

136 | Stochastic Optimal Control: The Discrete Time Case - Bertsekas, Shreve - 1978 |

127 | Dynamic programming and stochastic control - Bertsekas - 1976 |

29 |
Linear-quadratic programming and optimal control
- Rockafellar
- 1987
(Show Context)
Citation Context .... In optimal control only a relatively small class of linear-quadratic problems has traditionally received much attention, however. A much more general class has recently been explored by Rockafellar =-=[1]-=- with the aim of opening up a wide domain for application of techniques of large-scale linear and quadratic programming, in particular the finite generation method of Rockafellar and Wets [2], [3], [4... |

25 |
A Lagrangian finite generation technique for solving linearquadraiic problems in stochastic programming
- Rockafellar, Weis
(Show Context)
Citation Context ...lar [1] with the aim of opening up a wide domain for application of techniques of large-scale linear and quadratic programming, in particular the finite generation method of Rockafellar and Wets [2], =-=[3]-=-, [4] that has been implemented in stochastic programming [5]. Central to this purpose is the development of flexible problem formulations for which there is a strong duality theory that represents op... |

23 |
The optimal recourse problem in discrete time: L 1 -multipliers for inequality constraints
- Rockafellar, Wets
- 1978
(Show Context)
Citation Context ...tive involving only the control variables u0, u1, . . . , uT . This problem, with its block angular structure, is in the usual format for the multistage stochastic programs with recourse; see [11] or =-=[12]-=-, for example. Problem (Psto) revolves around the choice of the random variable u = (u0, u1, . . . , uT ), which can be regarded as a function from Ω to lR k 0 ×· · ·×lR k T and therefore as an elemen... |

7 |
Duality for stochastic programming interpreted as L.P. in Lp-space
- Eisner, Olsen
- 1975
(Show Context)
Citation Context ...ic objective involving only the control variables u0, u1, . . . , uT . This problem, with its block angular structure, is in the usual format for the multistage stochastic programs with recourse; see =-=[11]-=- or [12], for example. Problem (Psto) revolves around the choice of the random variable u = (u0, u1, . . . , uT ), which can be regarded as a function from Ω to lR k 0 ×· · ·×lR k T and therefore as a... |

5 |
Linear-quadratic programming problems with stochastic penalties: the finite generation algorithm
- Rockafellar, Wets
- 1986
(Show Context)
Citation Context ...1] with the aim of opening up a wide domain for application of techniques of large-scale linear and quadratic programming, in particular the finite generation method of Rockafellar and Wets [2], [3], =-=[4]-=- that has been implemented in stochastic programming [5]. Central to this purpose is the development of flexible problem formulations for which there is a strong duality theory that represents optimal... |

4 | A dual solution procedure for quadratic stochastic programs with simple recourse - Rockafellar, Wets - 1983 |

4 |
Symmetric dual quadratic programs
- Cottle
- 1963
(Show Context)
Citation Context ...thematical modeling. The basic facts about the relationship between (P) and (Q) can be derived from the standard theory of linear and quadratic programming, specifically the duality theorem of Cottle =-=[6]-=- and the existence theorem of Frank and Wolfe [7]. Theorem 2.1 (Rockafellar and Wets [3, Theorem 2]). If either (P) or (Q) has finite optimal value, or if both problems have feasible solutions, then b... |

3 |
Continuous programming part one: linear objectives
- Grinold
(Show Context)
Citation Context ...he kind in Theorem 3.5 were developed for continuous-time problems in Rockafellar [1]. They resemble conditions first detected in a special setting known as “continuous linear programming” by Grinold =-=[9]-=-. Besides being of interest in the study of what optimality might mean in a particular application modeled directly in terms of (Pdet) and (Qdet), the conditions in Theorem 3.5, like those in Theorem ... |

2 |
An implementation of the finite generation method
- King
- 1987
(Show Context)
Citation Context ...ion of techniques of large-scale linear and quadratic programming, in particular the finite generation method of Rockafellar and Wets [2], [3], [4] that has been implemented in stochastic programming =-=[5]-=-. Central to this purpose is the development of flexible problem formulations for which there is a strong duality theory that represents optimal trajectories and controls in terms of saddlepoints of a... |