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  • 1
    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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  • 2
    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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  • 3
    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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