Combining stochastic programming and optimal control to solve multistage stochastic optimization problems
In this contribution we propose an approach to solve a multistage stochastic programming problem which allows us to obtain a time and nodal decomposition of the original problem. This double decomposition is achieved applying a discrete time optimal control formulation to the original stochastic programming problem in arborescent form. Combining the arborescent formulation of the problem with the point of view of the optimal control theory naturally gives as a first result the time decomposability of the optimality conditions, which can be organized according to the terminology and structure of a discrete time optimal control problem into the systems of equation for the state and adjoint variables dynamics and the optimality conditions for the generalized Hamiltonian. Moreover these conditions, due to the arborescent formulation of the stochastic programming problem, further decompose with respect to the nodes in the event tree. The optimal solution is obtained by solving small decomposed subproblems and using a mean valued fixed-point iterative scheme to combine them. To enhance the convergence we suggest an optimization step where the weights are chosen in an optimal way at each iteration.
|Date of creation:||2011|
|Date of revision:||2011|
|Contact details of provider:|| Postal: Cannaregio, S. Giobbe no 873 , 30121 Venezia|
Web page: http://www.unive.it/dip.economia
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Diana Barro & Elio Canestrelli, 2009.
"Tracking error: a multistage portfolio model,"
Annals of Operations Research,
Springer, vol. 165(1), pages 47-66, January.
- Diana Barro & Elio Canestrelli, 2005. "Tracking Error: a multistage portfolio model," GE, Growth, Math methods 0510012, EconWPA.
- Diana Barro & Elio Canestrelli, 2005. "Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization," GE, Growth, Math methods 0510011, EconWPA.
- A. Ruszczynski, 1994. "On Augmented Lagrangian Decomposition Methods For Multistage Stochastic Programs," Working Papers wp94005, International Institute for Applied Systems Analysis.
- C.H. Rosa & A. Ruszczynski, 1994. "On Augmented Lagrangian Decomposition Methods for Multistage Stochastic Programs," Working Papers wp94125, International Institute for Applied Systems Analysis.
- Barro, Diana & Canestrelli, Elio, 2005. "Dynamic portfolio optimization: Time decomposition using the Maximum Principle with a scenario approach," European Journal of Operational Research, Elsevier, vol. 163(1), pages 217-229, May. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:ven:wpaper:2011_24. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Geraldine Ludbrook)
If references are entirely missing, you can add them using this form.