Stochastic optimization is a very broad research area, and I am particularly
interested in the problem of devising bounds on optimal solutions.
It is an important practical task, as for many
problems, it is possible to compare heuristic policies on the basis of
a simulation of their performance, while it is difficult to assess how close
to optimality these policies are.
- Approximate Linear Programming:
- I develop techniques to derive strong approximate linear programming
formulations of stochastic problems. Applications in routing,
natural gas storage, and finance.
- Chance Constrained Problems:
- I study reformulations of stochastic programs where some constraints
have random coefficients and must be satisfied with a given probability.
These problems are known as "stochastic programs with random
technology matrix". These reformulations yield non-convex trilinear programs
with a very specific structure. We study and implement algorithms to
solve this type of problems. Applications in revenue management, energy, and