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  • Stochastic integer programming  (1)
  • asymptotic stability  (1)
  • parametric optimization  (1)
  • 1
    Digitale Medien
    Digitale Medien
    On structure and stability in stochastic programs with random technology matrix and complete integer recourse (1995)
    Springer
    Mathematical programming 70 (1995), S. 73-89 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Stochastic integer programming ; Parametric integer programming ; Continuity ; Stability ; Weak convergence of probability measures
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585929
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    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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  • 3
    Digitale Medien
    Digitale Medien
    Some Aspects of Stability in Stochastic Programming (2000)
    Springer
    Annals of operations research 100 (2000), S. 55-84 
    Details
    ISSN: 1572-9338
    Schlagwort(e): stochastic programming ; parametric optimization ; stability analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019258932012
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