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TITLE: Advances in multistage optimization
SPEAKER: Dimitris Bertsimas (Boeing Prof. of OR)
ABSTRACT:
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)
Bio:
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.
