Acm270 Algebraic Techniques and Semidefinite Optimization

In this lecture, we will discuss one of the most important applications of semidefinite programming, namely its use in the formulation of convex relaxations of nonconvex optimization problems. We will present the results from several different, but complementary, points of view. These will also serve us as starting points for the generalizations to be presented later in the course. We will discuss first the case of binary quadratic optimization, since in this case the notation is simpler, and perfectly illustrates many of the issues appearing in more complicated problems. Afterwards, a more general formulation containing arbitrary linear and quadratic constraints will be presented.