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  • decomposition  (2)
  • Convergence  (1)
  • Key words: probabilistic programming – discrete distributions – generalized concavity – column generation Mathematics Subject Classification (1991): 90C15, 90C11, 65K05, 49M27  (1)
Source
Material
Years
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Feasible direction methods for stochastic programming problems (1980)
    Springer
    Mathematical programming 19 (1980), S. 220-229 
    Details
    ISSN: 1436-4646
    Keywords: Stochastic Programming ; Feasible Direction Methods ; Point-to-Set Maps ; Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A unified approach to stochastic feasible direction methods is developed. An abstract point-to-set map description of the algorithm is used and a general convergence theorem is proved. The theory is used to develop stochastic analogs of classical feasible direction algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581643
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Parallel decomposition of multistage stochastic programming problems (1993)
    Springer
    Mathematical programming 58 (1993), S. 201-228 
    Details
    ISSN: 1436-4646
    Keywords: Stochastic programming ; dynamic programming ; decomposition ; parallel computing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new decomposition method for multistage stochastic linear programming problems is proposed. A multistage stochastic problem is represented in a tree-like form and with each node of the decision tree a certain linear or quadratic subproblem is associated. The subproblems generate proposals for their successors and some backward information for their predecessors. The subproblems can be solved in parallel and exchange information in an asynchronous way through special buffers. After a finite time the method either finds an optimal solution to the problem or discovers its inconsistency. An analytical illustrative example shows that parallelization can speed up computation over every sequential method. Computational experiments indicate that for large problems we can obtain substantial gains in efficiency with moderate numbers of processors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581267
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On augmented Lagrangian decomposition methods for multistage stochastic programs (1996)
    Springer
    Annals of operations research 64 (1996), S. 289-309 
    Details
    ISSN: 1572-9338
    Keywords: Stochastic programming ; decomposition ; augmented Lagrangian ; Jacobi method ; parallel computation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A general decomposition framework for large convex optimization problems based on augmented Lagrangians is described. The approach is then applied to multistage stochastic programming problems in two different ways: by decomposing the problem into scenarios and by decomposing it into nodes corresponding to stages. Theoretical convergence properties of the two approaches are derived and a computational illustration is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187650
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Concavity and efficient points of discrete distributions in probabilistic programming (2000)
    Springer
    Mathematical programming 89 (2000), S. 55-77 
    Details
    ISSN: 1436-4646
    Keywords: Key words: probabilistic programming – discrete distributions – generalized concavity – column generation Mathematics Subject Classification (1991): 90C15, 90C11, 65K05, 49M27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00011393
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    Paper (German National Licenses)
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