In this work, we investigate the application of Davis–Yin splitting (DYS) to convex optimization problems and demonstrate that swapping the roles of the two nonsmooth convex functions can result in a faster convergence rate. Such a swap typically yields a different sequence of iterates, but its impact on convergence behavior has been largely understudied or … Read more
In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and the other continuous and weakly concave). We introduce a new splitting algorithm that extends the Davis-Yin splitting … Read more
In nonconvex optimisation, commonly used methods are usually shown to converge to stationary points, while guarantees of convergence to local minimisers have comparatively received less attention. To close this gap, we analyse the convergence behaviour of the Davis–Yin three-operator splitting method. More precisely, for structured weakly convex semialgebraic optimisation problems, we establish convergence to local … Read more