Tutorial given by Samuel Burer at the Summer School of the 20th Conference on Integer Programming and Combinatorial Optimization.
Abstract: Semidefinite programming (SDP) is a powerful modeling technique that extends both linear and second-order cone programming. In this tutorial, we discuss the basics of SDP, including applications, duality, algorithms, and software. We'll also cover various SDP relaxation techniques for combinatorial optimization problems such as MaxCut and maxiumum stable set, which are classical "success stories" in this area. Finally, we'll explore the boundary of current research, especially in the area of mixed-integer nonlinear programming.