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  • 1
    Digitale Medien
    Digitale Medien
    Distribution sensitivity in stochastic programming (1991)
    Springer
    Mathematical programming 50 (1991), S. 197-226 
    Details
    ISSN: 1436-4646
    Schlagwort(e): 90C15 ; 90C31 ; Stochastic programming ; quantitative stability ; recourse problem ; chance constrained problem ; probability metric
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01594935
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  • 2
    Digitale Medien
    Digitale Medien
    Metric regularity and quantitative stability in stochastic programs with probabilistic constraints (1999)
    Springer
    Mathematical programming 84 (1999), S. 55-88 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Key words: stochastic programming – probabilistic constraints – metric regularity – nonsmooth analysis – quadratic growth – quantitative stability – empirical approximation Mathematics Subject Classification (1991): 90C15, 90C30, 49J52
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s10107980016a
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  • 3
    Digitale Medien
    Digitale Medien
    Stability in multistage stochastic programming (1995)
    Springer
    Annals of operations research 56 (1995), S. 79-93 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02031701
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  • 4
    Digitale Medien
    Digitale Medien
    Unit commitment in power generation – a basic model and some extensions (2000)
    Springer
    Annals of operations research 96 (2000), S. 167-189 
    Details
    ISSN: 1572-9338
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1018947401538
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  • 5
    Digitale Medien
    Digitale Medien
    Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty (2000)
    Springer
    Annals of operations research 100 (2000), S. 251-272 
    Details
    ISSN: 1572-9338
    Schlagwort(e): multistage stochastic programming ; mixed-integer ; Lagrangian relaxation ; power management ; stochastic unit commitment
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain demand (or load) is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints coupling power units. It is assumed that the stochastic load process is given (or approximated) by a finite number of realizations (scenarios) in scenario tree form. Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single (thermal or hydro) unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the first stage (primal) decisions starting from the optimal (stochastic) multipliers is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 200 000 binary and 350 000 continuous variables, and more than 500 000 constraints.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019248506301
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  • 6
    Digitale Medien
    Digitale Medien
    Stability analysis for stochastic programs (1991)
    Springer
    Annals of operations research 30 (1991), S. 241-266 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Stochastic programs with recourse ; stochastic programs with probabilistic constraints ; distribution sensitivity ; probability metrics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02204819
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  • 7
    Digitale Medien
    Digitale Medien
    A simple recourse model for power dispatch under uncertain demand (1995)
    Springer
    Annals of operations research 59 (1995), S. 135-164 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Power dispatch under uncertainty ; stochastic programming ; asymptotic stability
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02031746
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  • 8
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    Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets (2013)
    Details
    Publikationsdatum: 2021-03-16
    Beschreibung: The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 9
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    Szenariogenerierung zur Modellierung der stochastischen Ausspeiselasten in einem Gastransportnetz (2011)
    Details
    Publikationsdatum: 2020-08-05
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 10
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    Optimale Blockauswahl bei der Kraftwerkseinsatzplanung (1996)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: The paper addresses the unit commitment problem in power plant operation planning. For a real power system comprising coal and gas fired thermal as well as pumped storage hydro plants a large-scale mixed integer optimization model for unit commitment is developed. Then primal and dual approaches to solving the optimization problem are presented and results of test runs are reported.
    Schlagwort(e): ddc:000
    Sprache: Deutsch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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