2,147 research outputs found
Regularized Decomposition of High-Dimensional Multistage Stochastic Programs with Markov Uncertainty
We develop a quadratic regularization approach for the solution of
high-dimensional multistage stochastic optimization problems characterized by a
potentially large number of time periods/stages (e.g. hundreds), a
high-dimensional resource state variable, and a Markov information process. The
resulting algorithms are shown to converge to an optimal policy after a finite
number of iterations under mild technical assumptions. Computational
experiments are conducted using the setting of optimizing energy storage over a
large transmission grid, which motivates both the spatial and temporal
dimensions of our problem. Our numerical results indicate that the proposed
methods exhibit significantly faster convergence than their classical
counterparts, with greater gains observed for higher-dimensional problems
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Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
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.Stochastic programming, discrete time control problem, decomposition methods, iterative scheme
Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization
We propose a decomposition method for the solution of a dynamic portfolio optimization problem which fits the formulation of a multistage stochastic programming problem. The method allows to obtain time and nodal decomposition of the problem in its arborescent formulation applying a discrete version of Pontryagin Maximum Principle. The solution of the decomposed problems is coordinated through a fixed- point weighted iterative scheme. The introduction of an optimization step in the choice of the weights at each iteration allows to solve the original problem in a very efficient way.Stochastic programming, Discrete time optimal control problem, Iterative scheme, Portfolio optimization
An interior-point and decomposition approach to multiple stage stochastic programming
There is no abstract of this report
A parallel computation approach for solving multistage stochastic network problems
The original publication is available at www.springerlink.comThis paper presents a parallel computation approach for the efficient solution of very
large multistage linear and nonlinear network problems with random parameters. These
problems result from particular instances of models for the robust optimization of network
problems with uncertainty in the values of the right-hand side and the objective function
coefficients. The methodology considered here models the uncertainty using scenarios to
characterize the random parameters. A scenario tree is generated and, through the use of
full-recourse techniques, an implementable solution is obtained for each group of scenarios
at each stage along the planning horizon.
As a consequence of the size of the resulting problems, and the special structure of their
constraints, these models are particularly well-suited for the application of decomposition
techniques, and the solution of the corresponding subproblems in a parallel computation
environment. An augmented Lagrangian decomposition algorithm has been implemented
on a distributed computation environment, and a static load balancing approach has been
chosen for the parallelization scheme, given the subproblem structure of the model. Large
problems – 9000 scenarios and 14 stages with a deterministic equivalent nonlinear model
having 166000 constraints and 230000 variables – are solved in 45 minutes on a cluster of
four small (11 Mflops) workstations. An extensive set of computational experiments is
reported; the numerical results and running times obtained for our test set, composed of
large-scale real-life problems, confirm the efficiency of this procedure.Publicad
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