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  • 1
    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
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    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
    Library Location Call Number Volume/Issue/Year Availability
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