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  • 1
    Digitale Medien
    Digitale Medien
    Feasible direction methods for stochastic programming problems (1980)
    Springer
    Mathematical programming 19 (1980), S. 220-229 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Stochastic Programming ; Feasible Direction Methods ; Point-to-Set Maps ; Convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581643
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  • 2
    Digitale Medien
    Digitale Medien
    Parallel decomposition of multistage stochastic programming problems (1993)
    Springer
    Mathematical programming 58 (1993), S. 201-228 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Stochastic programming ; dynamic programming ; decomposition ; parallel computing
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581267
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  • 3
    Digitale Medien
    Digitale Medien
    On augmented Lagrangian decomposition methods for multistage stochastic programs (1996)
    Springer
    Annals of operations research 64 (1996), S. 289-309 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Stochastic programming ; decomposition ; augmented Lagrangian ; Jacobi method ; parallel computation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02187650
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  • 4
    Digitale Medien
    Digitale Medien
    On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse (1998)
    Springer
    Mathematical methods of operations research 47 (1998), S. 39-49 
    Details
    ISSN: 1432-5217
    Schlagwort(e): Stochastic Programming ; Empirical Measures ; Uniform Convergence ; Value Functions of Mixed-Integer Linear Programs
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01193835
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