Speaker
Description
A number of interesting optimization problems is nonconvex and thus hard to optimize, particularly if the optimization variable is additionally high- or infinite-dimensional (e.g. a function on some domain). Often the nonconvexity is associated with some kind of discreteness or sparsity: For instance, the function to be optimized may only assume particular values or has sparse support. A typical strategy then is to instead solve a simpler, relaxed problem (for instance integer programs are often reduced to corresponding linear programs), which usually convexifies (part of) the optimization problem. Using the example of so-called branched transport, a nonconvex version of optimal transport, I will illustrate a few convexification concepts and associated numerical methods.
