Semidefinite optimization

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...

Some Applications of Semidefinite Optimization from an Operations Research Viewpoint

Semidefinite programs and combinatorial optimization

7 Constraint generation and quadratic inequalities 29 7.1 Example: the stable set polytope again . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2 Strong insolvability of quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . 30 7.3 Inference rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7.4 Algorithmic aspects of inference rules . ...

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 ...