In this tutorial, we will start by discussing some of the basic ideas and techniques that allow a discrete optimization problem to be relaxed or immersed into a continuous optimization problem. Typically, the resulting continuous optimization problem is convex, implying strong properties of duality and efficiency. As part of the first lecture, we will review convexification ideas and strong duality in the context of cone optimization problems. The second and third lectures will focus on many approaches for going back from the continuous problem to the discrete problem, i.e. rounding a solution from the larger, continuous problem into a solution to the discrete problem. This is a very rich area, and we will survey a variety of techniques.
The first session of this mini course will take place on Monday, August 21 from 9:30 - 10:30 AM; the second session of this mini course will take place on Monday, August 21 from 11:00 AM - 12:00 PM; and the third session of this mini course will take place on Tuesday, August 22 from 9:30 - 10:30 AM.