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  • Convergence  (1)
  • Key words: probabilistic programming – discrete distributions – generalized concavity – column generation Mathematics Subject Classification (1991): 90C15, 90C11, 65K05, 49M27  (1)
  • Uniform Convergence  (1)
Material
Years
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 19 (1980), S. 220-229 
    ISSN: 1436-4646
    Keywords: Stochastic Programming ; Feasible Direction Methods ; Point-to-Set Maps ; Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 89 (2000), S. 55-77 
    ISSN: 1436-4646
    Keywords: Key words: probabilistic programming – discrete distributions – generalized concavity – column generation Mathematics Subject Classification (1991): 90C15, 90C11, 65K05, 49M27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.
    Type of Medium: Electronic Resource
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  • 3
    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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