Full Length Paper Series B

Mathematical Programming

, Volume 134, Issue 1, pp 5-22

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Semidefinite optimization in discrepancy theory


Recently, there have been several new developments 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.


Semidefinite optimization Discrepancy theory Rounding error Algorithms

Mathematics Subject Classification

90 05