A forward-backward algorithm with different inertial terms for the minimization of the sum of two non-convex functions

Szilárd Csaba László

Published 2020-02-16Version 1

We investigate an inertial forward-backward algorithm in connection with the minimization of the sum of a non-smooth and possible non-convex and a non-convex differentiable function. The algorithm is formulated in the spirit of the famous FISTA method, however the setting is non-convex and we allow different inertial terms. We also treat the case when the non-smooth function is convex and we show that in this case a better step-size can be allowed. We prove some abstract convergence results which applied to our numerical scheme allow us to show that the generated sequences converge to a critical point of the objective function, provided a regularization of the objective function satisfies the Kurdyka-{\L}ojasiewicz property.