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Responsible lecturer: C. Fábián, professor (

Assumed preliminary studies
Linear and Nonlinear Programming


  1. Stochastic programming problem examples. Classification, static and dynamic models.
    Definition of constraints and objective by expected value or probability. Definition and solution of the newsboy problem.
  2. Static models (mean / variance model (Markowitz 1952), mean / risk models; probability constraints (Charnes, Cooper 1963, Prékopa 1970); Value-at-Risk minimization (Kataoka 1963); constraints including conditional expected value (Prékopa 1970), integrated chance constraints (Klein Haneveld 1986))
    Convexity solutions: proofs in case of expected values and probabilities.
  3. The simple recourse problem (Dantzig 1955, Beale 1955) 
    Definition and mathematical description. Solution methods for discrete distribution: primal method (Wets 1983), dual method (Prékopa 1990). 
    Solution method for continuous distribution functions: : cutting-plane, bundle, and level type methods.
  4. Logconcave metrics and functions
    Fundamentals of logconcave metrics (Prékopa 1971). 
    Examples for logconcave density functions. 
    Logconcave property of probability constraints (Prékopa 1973).
  5. Two stage models
    Traditional definition (Dantzig, Madansky 1961), mathematical description (Wets 1974). 
    Discretization methods (Kall 1980). 
    Decomposition methods for the case of discrete distributions
  6. Multistage models
    Definition, mathematical description, skeleton of solution methods.

Kall, P., Wallace, S.W., Stochastic Programming, Wiley, 1994. 
Prékopa A., Stochastic Programming, Kluwer, 1995. 
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer, 1997-1999.