Advances in multistage optimization

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TITLE:  Advances in multistage optimization

SPEAKER:  Dimitris Bertsimas (Boeing Prof. of OR)


In this presentation, we show a significant role that symmetry, a fundamental concept in convex geometry, plays in determining the power of robust and finitely adaptable solutions in multi-stage stochastic and adaptive optimization problems. We consider a fairly general class of multi-stage mixed integer stochastic and adaptive optimization problems and propose a good approximate solution policy with performance guarantees that depend on the
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.


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