Tutte Colloquium - Ting Kei Pong

Splitting methods are popular approaches for finding a point in the

intersection of two closed convex sets and have also been applied

successfully to various nonconvex instances, even though the theoretical

justification in this latter setting is far from being complete. In this

talk, we discuss the Douglas Rachford and the Peaceman Rachford splitting methods, which have been extensively studied in the convex scenario, for finding the intersection of a closed convex set and a possibly nonconvex closed set. We establish, for the first time, the global convergence of the sequence generated to a stationary point of a certain optimization problem under mild assumptions on the sets and the stepsize. Our convergence analysis relies on a specially constructed new merit function. We also compare numerically the splitting methods with the alternating projection method on finding sparse vectors in an affine set.

This is joint work with Guoyin Li.