Incremental Subgradients for Constrained Convex Optimization: A Unified Framework and New Methods

Abstract

We present a unifying framework for nonsmooth convex minimization bringing together $\epsilon$-subgradient algorithms and methods for the convex feasibility problem. This development is a natural step for $\epsilon$-subgradient methods in the direction of constrained optimization since the Euclidean projection frequently required in such methods is replaced by an approximate projection, which is often easier to compute. The developments are applied to incremental subgradient methods, resulting in new algorithms suitable to large-scale optimization problems, such as those arising in tomographic imaging.