Friday, October 28, 2005
1:30 pm Posner Hall 151
Dimitris Bertsimas
Sloan School of Management, MIT
Robust and Adaptive Optimization: A Tractable Approach to Optimization under Uncertainty
For almost all its history, the predominant model in Operations Research to describe uncertainty is probability theory. Optimization under uncertainty, however, when the primitive elements are probability distributions suffers from the curse of dimensionality, and thus it does not have a tractable theory.
We show that when the primitive elements to describe uncertainty are polyhedral or conic uncertainty sets, the central models of optimization (linear, mixed integer, conic) under uncertainty, models known as robust optimization, can be reformulated as optimization problems of the same structure and a mild increase in the dimension, and thus are tractably solvable both practically and theoretically. We also show how to construct uncertainty sets from data and risk preferences.
We further describe adaptive optimization, a tractable theory for optimization under uncertainty with recourse when uncertainty is described via uncertainty sets.
We finally present applications of these methods to: optimal control, inventory theory and multiperiod asset allocation.
