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