Technion, IEM faculty - Bi-weekly Faculty Workshop Speaker: Eden Chlamtac Title: Convex Programming Hierarchies: Trading Time for Approximation Date: 04/12/2011 Time: 11:30 Place: Bloomfield-527 Abstract: <http://ie.technion.ac.il/seminar_files/1322582330_eden.doc> Or simply read this: Convex optimization tools, such as linear programming (LP) and semidefinite programming (SDP), have become ubiquitous in the field of combinatorial approximation algorithms in the last few decades. Given a combinatorial optimization problem (e.g. Maximum Stable Set), a standard approach to obtain an approximation algorithm is as follows: formulate the problem as an integer program (IP), relax this formulation to an LP or SDP, solve the relaxation, and then "round" the solution back to an integer solution. This approach is limited by how well the convex program (LP or SDP) approximates the original IP formulation, i.e. the integrality gap. One way to circumvent this limitation is through hierarchies of convex programs (so -called lift-and-project methods), which give a systematic way of iteratively strengthening any relaxation (at the cost of increased running time to solve it), so that the integrality gap gradually decreases. While initially, most of the literature on hierarchies in the context of approximation algorithms had focused on impossibility results, there has been a surprising surge of recent positive results. I will survey this recent development, by describing a number of combinatorial optimization problems for which we have been able to achieve improved approximations using hierarchies. --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <ehazan@ie.technion.ac.il>