Spring 2015 Seminar Series

DATE: 2/5/15
LOCATION: E51-395
TIME: 4:15pm
Reception immediately following

SPEAKER:
Aharon Ben-Tal

TITLE
Some Remedies for Some Intractable Optimization Problems

ABSTRACT
The need to solve real-life optimization problems poses frequently a severe challenge, as the underlying mathematical programs threaten to be intractable. The intractability can be attributed to any of the following properties: large dimensionality of the design dimension; lack of convexity; parameters affected by uncertainty. In problems of designing optimal mechanical structures (truss topology design, shape design, free material optimization), the mathematical programs typically has a large dimensional Semi Definite Program. Some Signal Processing and Estimation problems may result in nonconvex formulations. In the wide area of optimization under uncertainty, some classical approaches, such as chance (probabilistic) constraints, give rise to nonconvex NP-hard problems. In all the above applications we explain how the difficulties were resolved. In some cases this was achieved by mathematical analysis (notoriously duality theory) which converted the problems (or its dual) to a tractable convex program. In the Robust Control example, a reparameterization scheme is developed under which the problem is converted to a tractable deterministic convex program.