Responsible lecturer: C. Fábián, professor (fabian.csaba@nje.hu)
Assumed preliminary studies:
Linear and Nonlinear Programming
Topics:
- 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. - 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. - 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. - Logconcave metrics and functions
Fundamentals of logconcave metrics (Prékopa 1971).
Examples for logconcave density functions.
Logconcave property of probability constraints (Prékopa 1973). - Two stage models
Traditional definition (Dantzig, Madansky 1961), mathematical description (Wets 1974).
Discretization methods (Kall 1980).
Decomposition methods for the case of discrete distributions - Multistage models
Definition, mathematical description, skeleton of solution methods.
Literature:
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.