Advances in multistage optimization
TITLE: Advances in multistage optimization
SPEAKER: Dimitris Bertsimas (Boeing Prof. of OR)
In this presentation, we show a significant role that symmetry, a
concept in convex geometry, plays in determining the power of robust
finitely adaptable solutions in multi-stage stochastic and adaptive
optimization problems. We consider a fairly general class of
integer stochastic and adaptive optimization problems and propose a
approximate solution policy with performance guarantees that depend on
geometric properties such as symmetry of the uncertainty sets. In particular, we show that a class of finitely adaptable solutions is a good approximation for both the multi-stage stochastic as well as the adaptive optimization problem. A finitely adaptable solution specifies a small set of solutions for each stage and the solution policy implements the best solution from the given
set depending on the realization of the uncertain parameters in the past stages. To the best of our knowledge, these are the first approximation results for the multi-stage problem in such generality. (joint work with Vineet Goyal, Columbia University and Andy Sun, MIT)
Dimitris Bertsimas is currently the Boeing Professor of Operations Research and the
codirector of the Operations Research Center at the Massachusetts Institute of Technology.
He has received a BS in Electrical Engineering and Computer Science at the National
Technical University of Athens, Greece in 1985, a MS in Operations Research at MIT in
1987, and a Ph.D in Applied Mathematics and Operations Research at MIT in 1988.
Since 1988, he has been in the MIT faculty.