Semidefinite optimization in discrepancy theory

Semidefinite optimization in discrepancy theory

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 ...

Semidefinite Optimization

Semidefinite Optimization ∗

Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential inclusion, and obtaining tight bounds...

Semidefinite programming in combinatorial optimization

We discuss the use of semidefinite programming for combinatorial optimization problems. The main topics covered include (i) the Lovfisz theta function and its applications to stable sets, perfect graphs, and coding theory. (it) the automatic generation of strong valid inequalities, (iii) the maximum cut problem and related problems, and (iv) the embedding of finite metric spaces and its relatio...

Upper Bounds in Discrepancy Theory

Through the use of a few examples, we shall illustrate the use of probability theory, or otherwise, in the study of upper bound questions in the theory of irregularities of point distribution. Such uses may be Monte Carlo in nature but the most efficient ones appear to be quasi Monte Carlo in nature. Furthermore, we shall compare the relative merits of probabilistic and non-probabilistic techni...