Projection-free methods and their applications

Projection-free methods have attracted much attention in both machine learning and optimization communities recently. These simple methods can guarantee the generation of sparse solutions. In addition, without the computation of full gradients, they can handle huge-scale problems sometimes even with an exponentially increasing number of decision variables.  In this talk, we provide an overview of projection-free methods starting from the classic conditional gradient (a.k.a. Frank-Wolfe method) and a few of its variants. We present some new conditional gradient methods for solving convex optimization problems with general affine and nonlinear constraints in order to significantly expand the application areas of these methods. We illustrate the advantages of projection-free methods for solving an important class of radiation therapy treatment planning problems arising from healthcare industry.