On the Linear Convergence of the Approximate Proximal Splitting Method for Non-Smooth Convex Optimization

Understand

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth.

• In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization problems.
• Methods in the APS class include many well-known algorithms such as the proximal splitting method (PSM), the block coordinate descent method (BCD) and the approximate gradient projection methods for smooth convex optimization.
• We establish the linear convergence of APS methods under a local error bound assumption.