Marie Miller: The duality and efficiency in semidefinite programming

The purpose of this thesis is to explore the aspect of duality and efficiency in semidefinite programming. In particular, we discuss bad behaved systems in relation to the duality gap. In that sense, the impact of efficiency seems to be dependent of if there exists duality gap. There are several approaches to close up it, and we present two regularization algorithms. The first algorithm is based on abstract convex programming, and the second by semidefinite programing. The analysis part will end by some semidefinite programming problems.