Variational Analysis and Optimization Seminar

We propose a Bregman inertial forward-reflected-backward method for nonconvex composite problems. Our analysis relies on a novel approach that imposes general conditions on implicit merit function parameters, which yields a stepsize condition that is independent of inertial parameters. In turn, a question of Malitsky and Tam regarding whether FRB can be equipped with a Nesterov-type acceleration is resolved. Assuming the generalized concave Kurdyka-Lojasiewicz property of a quadratic regularization of the objective, we obtain sequential convergence as well as convergence rates on both the function value and actual sequence. Joint work with Ziyuan Wang Speaker(s): Shawn Wang (University of British Columbia - Canada)