CONVERGENCE PROPERTIES OF PROXIMAL (SUB)GRADIENT METHODS WITHOUT CONVEXITY OR SMOOTHNESS OF ANY OF THE FUNCTIONS

We establish convergence properties for a framework that includes a variety of proximal subgradient methods, where none of the involved functions needs to be convex or differentiable. The functions are assumed to be Clarke-regular. Our results cover the projected and conditional variants for the constrained case, the use of the inertial/momentum terms, and incremental methods when each of the functions is itself a sum, and the methods process the components in this sum separately.