MA662 Stochastic Optimization
Course Catalog Description
1. Ability to formulate an appropriate optimization model for a decision making
problem involving uncertain parameters.
2. Knowledge of the mathematical models of stochastic optimization; their structure, advantages, and limitations.
3. Knowledge of the mathematical models of risk-averse optimization and the relations between them.
4. Knowledge of the numerical approaches for solving problems with constraints on probability of events, stochastic-order constraints, two- and multi-stage problems.
5. Understanding of time-consistency for dynamic risk.
6. Understanding the statistical meaning of the optimal value and solution for stochastic optimization problems based on sampled data.
There is no required textbook; lecture notes will be distributed in class. The following are supplementary books:
- A. Shapiro, D. Dentcheva, A. Ruszczynski: Lecture Notes on Stochastic Programming Modeling and Theory, SIAM and MPS, Second Edition 2014.The first edition is available online.
- A. Ruszczynski and A. Shapiro, Stochastic Programming, Handbook in Operations Research and Management Science, Elsevier Science, Amsterdam, 2003
- Andras Prekopa, Stochastic Programming, Kluwer Academic Publishers, Netherlands, 1995
A student's course grade will be based on 7-8 assignments.
|Week 1||Modeling issues in presence of uncertainty and risk.|
|Week 2||Optimization problem with probabilistic (chance) constraints: properties.|
|Week 3||Numerical solution of optimization problems with probabilistic constraints.|
|Week 4||Calculating bounds on probability of events.|
|Week 5||Stochastic optimization with recourse. Properties of the expected value functional. The structure of stochastic models with recourse.|
|Week 6||Numerical methods for solving two-stage problems.|
|Week 7||Multistage stochastic problems and their properties.|
|Week 8||Numerical techniques for multistage models.|
|Week 9||Risk-averse optimization:stochastic-order constraints.|
|Week 10||Numerical methods for problem with stochastic-order constraints|
|Week 11||Optimization problems with coherent measures of risk.|
|Week 12||Dynamic measures of risk. Time consistency.|
|Week 13||Optimization of dynamic measures of risk.|
|Week 14||Statistical aspects of stochastic optimization models.|