Decomposition of large-scale stochastic optimal control problems

Kengy Barty; Pierre Carpentier; Pierre Girardeau

RAIRO - Operations Research (2010)

  • Volume: 44, Issue: 3, page 167-183
  • ISSN: 0399-0559

Abstract

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In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework of our approach and present promising numerical results on a simplified power management problem.

How to cite

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Barty, Kengy, Carpentier, Pierre, and Girardeau, Pierre. "Decomposition of large-scale stochastic optimal control problems." RAIRO - Operations Research 44.3 (2010): 167-183. <http://eudml.org/doc/250825>.

@article{Barty2010,
abstract = { In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework of our approach and present promising numerical results on a simplified power management problem. },
author = {Barty, Kengy, Carpentier, Pierre, Girardeau, Pierre},
journal = {RAIRO - Operations Research},
keywords = {Stochastic optimal control; decomposition methods; dynamic programming; stochastic optimal control},
language = {eng},
month = {7},
number = {3},
pages = {167-183},
publisher = {EDP Sciences},
title = {Decomposition of large-scale stochastic optimal control problems},
url = {http://eudml.org/doc/250825},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Barty, Kengy
AU - Carpentier, Pierre
AU - Girardeau, Pierre
TI - Decomposition of large-scale stochastic optimal control problems
JO - RAIRO - Operations Research
DA - 2010/7//
PB - EDP Sciences
VL - 44
IS - 3
SP - 167
EP - 183
AB - In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework of our approach and present promising numerical results on a simplified power management problem.
LA - eng
KW - Stochastic optimal control; decomposition methods; dynamic programming; stochastic optimal control
UR - http://eudml.org/doc/250825
ER -

References

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  1. K.J. Arrow, L. Hurwicz and H. Uzawa, Studies in linear and nonlinear programming. Stanford University Press (1958).  
  2. Z. Artstein, Sensitivity to σ-fields of information in stochastic allocation. Stoch. Stoch. Rep.36 (1991) 41–63.  
  3. R. Bellman and S.E. Dreyfus, Functional approximations and dynamic programming. Math. Tables Other Aides comput.13 (1959) 247–251.  
  4. R. Bellman, Dynamic programming, Princeton University Press. New Jersey (1957).  
  5. D.P. Bertsekas, Dynamic programming and optimal control, 2nd edition, Vol. 1 & 2, Athena Scientific (2000).  
  6. K. Barty, J.-S. Roy and C. Strugarek, A stochastic gradient type algorithm for closed loop problems. Math. Program. (2007).  
  7. J. Blomvall and A. Shapiro, Solving multistage asset investment problems by the sample average approximation method. Math. Program.108 (2006) 571–595.  
  8. D.P. Bertsekas and J.N. Tsitsiklis, Neuro-Dynamic Programming, Athena Scientific (1996).  
  9. G. Cohen and J.-C. Culioli, Decomposition Coordination Algorithms for Stochastic Optimization. SIAM J. Control Optim.28 (1990) 1372–1403.  
  10. G. Cohen, Auxiliary Problem Principle and decomposition of optimization problems. J. Optim. Theory Appl. (1980) 277–305.  
  11. J.M. Danskin, The theory of max-min. Springer, Berlin (1967).  
  12. D.P. de Farias and B. Van Roy, The Linear Programming Approach to Approximate Dynamic Programming. Oper. Res.51 (2003) 850–856.  
  13. I. Ekeland and R. Temam, Convex analysis and variational problems. SIAM, Philadelphia (1999).  
  14. P. Girardeau, A comparison of sample-based Stochastic Optimal Control methods. E-print available at: arXiv:1002.1812v1, 2010.  
  15. H. Heitsch, W. Römisch and C. Strugarek, Stability of multistage stochastic programs. SIAM J. Optim.17 (2006) 511–525.  
  16. J.L. Higle and S. Sen, Stochastic decomposition. Kluwer, Dordrecht (1996).  
  17. T. Pennanen, Epi-convergent discretizations of multistage stochastic programs. Math. Oper. Res.30 (2005) 245–256.  
  18. A. Prékopa, Stochastic programming, Kluwer, Dordrecht (1995).  
  19. A. Shapiro, On complexity of multistage stochastic programs. Oper. Res. Lett.34 (2006) 1–8.  
  20. A. Shapiro and A. Ruszczynski (Eds.), Stochastic Programming, Elsevier, Amsterdam (2003).  
  21. C. Strugarek, Approches variationnelles et autres contributions en optimisation stochastique, Thèse de doctorat, École Nationale des Ponts et Chaussées, 5 (2006).  
  22. A. Turgeon, Optimal operation of multi-reservoir power systems with stochastic inflows. Water Resour. Res.16 (1980) 275–283.  
  23. J.N. Tstsiklis and B. Van Roy, Feature-based methods for large scale dynamic programming. Mach. Lear.22 (1996) 59–94.  

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