Semidefinite optimization in discrepancy theory

Abstract

Recently, there have been several newdevelopments in discrepancy theory based on connections to semidefinite programming. This connection has been useful in several ways. It gives efficient polynomial time algorithms for several problems for which only non-constructive results were previously known. It also leads to several new structural results in discrepancy itself, such as tightness of the so-called determinant lower bound, improved bounds on the discrepancy of the union of set systems and so on. We will give a brief survey of these results, focussing on the main ideas and the techniques involved. © The Author(s) 2012.