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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 70 (1995), S. 73-89 
    ISSN: 1436-4646
    Keywords: Stochastic integer programming ; Parametric integer programming ; Continuity ; Stability ; Weak convergence of probability measures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For two-stage stochastic programs with integrality constraints in the second stage, we study continuity properties of the expected recourse as a function both of the first-stage policy and the integrating probability measure. Sufficient conditions for lower semicontinuity, continuity and Lipschitz continuity with respect to the first-stage policy are presented. Furthermore, joint continuity in the policy and the probability measure is established. This leads to conclusions on the stability of optimal values and optimal solutions to the two-stage stochastic program when subjecting the underlying probability measure to perturbations.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 50 (1991), S. 197-226 
    ISSN: 1436-4646
    Keywords: 90C15 ; 90C31 ; Stochastic programming ; quantitative stability ; recourse problem ; chance constrained problem ; probability metric
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, stochastic programming problems are viewed as parametric programs with respect to the probability distributions of the random coefficients. General results on quantitative stability in parametric optimization are used to study distribution sensitivity of stochastic programs. For recourse and chance constrained models quantitative continuity results for optimal values and optimal solution sets are proved (with respect to suitable metrics on the space of probability distributions). The results are useful to study the effect of approximations and of incomplete information in stochastic programming.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 96 (2000), S. 167-189 
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract For the unit commitment problem in the hydro-thermal power system of VEAG Vereinigte Energiewerke AG Berlin we present a basic model and discuss possible extensions where both primal and dual solution approaches lead to flexible optimization tools. Extensions include staggered fuel prices, reserve policies involving hydro units, nonlinear start-up costs, and uncertain load profiles.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 30 (1991), S. 241-266 
    ISSN: 1572-9338
    Keywords: Stochastic programs with recourse ; stochastic programs with probabilistic constraints ; distribution sensitivity ; probability metrics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract For stochastic programs with recourse and with (several joint) probabilistic constraints, respectively, we derive quantitative continuity properties of the relevant expectation functionals and constraint set mappings. This leads to qualitative and quantitative stability results for optimal values and optimal solutions with respect to perturbations of the underlying probability distributions. Earlier stability results for stochastic programs with recourse and for those with probabilistic constraints are refined and extended, respectively. Emphasis is placed on equipping sets of probability measures with metrics that one can handle in specific situations. To illustrate the general stability results we present possible consequences when estimating the original probability measure via empirical ones.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 100 (2000), S. 55-84 
    ISSN: 1572-9338
    Keywords: stochastic programming ; parametric optimization ; stability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measures as a backbone we discuss qualitative and quantitative stability of recourse models that possibly involve integer variables. We sketch stability in chance constrained stochastic programming and provide some applications in statistical estimation. Finally, an outlook is devoted to issues that were not discussed in detail and to some open problems.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 59 (1995), S. 135-164 
    ISSN: 1572-9338
    Keywords: Power dispatch under uncertainty ; stochastic programming ; asymptotic stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Optimal power dispatch under uncertainty of power demand is tackled via a stochastic programming model with simple recourse. The decision variables correspond to generation policies of a system comprising thermal units, pumped storage plants and energy contracts. The paper is a case study to test the kernel estimation method in the context of stochastic programming. Kernel estimates are used to approximate the unknown probability distribution of power demand. General stability results from stochastic programming yield the asymptotic stability of optimal solutions. Kernel estimates lead to favourable numerical properties of the recourse model (no numerical integration, the optimization problem is smooth convex and of moderate dimension). Test runs based on real-life data are reported. We compute the value of the stochastic solution for different problem instances and compare the stochastic programming solution with deterministic solutions involving adjusted demand portions.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 47 (1998), S. 39-49 
    ISSN: 1432-5217
    Keywords: Stochastic Programming ; Empirical Measures ; Uniform Convergence ; Value Functions of Mixed-Integer Linear Programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 8
    Title: ¬A¬ Note on Preprocessing via Fourier-Motzkin Elimination in Two-Stage Stochastic Programming /; Preprint SC 96-32
    Author: Schultz, Rüdiger
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 1996
    Pages: 16 S.
    Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 96-32
    ISSN: 0933-7911
    Type of Medium: Book
    Language: English
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  • 9
    Title: On the Glivenko-Cantelli Problem in Stochastic Programming: Mixed-Integer Linear Recourse /; Preprint SC 97-04
    Author: Pflug, Georg Ch.
    Contributer: Ruszczynski, Andrzej , Schultz, Rüdiger
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 1997
    Pages: 16 S.
    Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 97-04
    ISSN: 0933-7911
    Type of Medium: Book
    Language: English
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  • 10
    Book
    Book
    Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Title: Discontinuous Optimization Problems in Stochastic Integer Programming /; Preprint SC 95-20
    Author: Schultz, Rüdiger
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 1995
    Pages: 12 S.
    Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 95-20
    ISSN: 0933-7911
    Type of Medium: Book
    Language: English
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