MA662 Stochastic Optimization
Course Catalog Description
The methodology of optimal operation of stochastic systems is known as stochastic
programming or stochastic optimization. It is a rapidly developing part of applied
mathematics based on probability theory, statistics, mathematical optimization and
optimal control. The main purpose of this course is to introduce students to the basic
models of optimal decisions under uncertainty and risk. We shall discuss various
modeling approaches, some basic properties of the models, as well as numerical
methods for their solution. The theory will be illustrated by applied problems.
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
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
- 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,
A student's course grade will be based on 7-8 assignments.
||Modeling issues in presence of uncertainty and risk.
||Optimization problem with probabilistic (chance) constraints:
| Week 3
||Numerical solution of optimization problems with probabilistic
| 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.