Math 517A – Optimization Under Uncertainty:

A First Course in Stochastic Programming

Lisa Korf

Spring 2002, MWF 12:30-1:20

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Outline of Course:

• Introduction to Stochastic Programming
• Stochastic programs with recourse
• Convexity, duality, optimality conditions
• The L-Shaped method and approximation issues
• Stochastic programs with chance constraints
• Further methods: Stochastic quasi-gradient
• Duality and contingent prices
• Existence and interpretation of contingent prices
• The Progressive Hedging Algorithm
• Multistage stochastic programming
• Further topics

Course Description: Almost every practical decision is made in the midst of some uncertainty about what will take place in the future that might affect the "value" of that decision. How does one formulate such a problem mathematically? The stochastic programming approach to decision making under uncertainty assigns a probability distribution to the uncertain parameters in an optimization problem. This approach is robust because it takes into account the effects of the possible future outcomes. However, such problems are inherently very large, so understanding and exploiting their underlying structure becomes very important from the perspective of

computation.

In this course, we will address how to practically model various types of problems in a structural optimization framework that may eventually be exploited in computational schemes. Theory and algorithms will be emphasized, and students will have a chance to model and solve practical problems to gain insight into the current capabilities in this quickly growing field. Throughout the class, the emphasis will be on applications to such diverse and interesting areas as capacity planning, inventory control, vehicle routing, water resources, forestry, energy, and finance.