Mixed Integer Semidefinite Programming - Theory and Algorithms

Mixed-integer semidefinite programming can be viewed as a generalization of mixed-integer programming where the vector of variables is replaced by mixed-integer positive semidefinite matrix variables. The combination of positive semidefiniteness and integrality allows to formulate various nonlinear optimization problems as (linear) mixed-integer semidefinite programs (MISDPs). Although MISDPs appeared already in the last century, they received little attention until recently. In this talk we present new results on MISDPs and resulting continuous relaxations. Finally, we present novel approaches for solving MISDPs.