On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces
For researchers working on convex feasibility problems, this work offers a theoretically grounded method to handle inconsistent cases, though it is an incremental improvement over existing subgradient projection techniques.
The paper proposes a self-adapting strategy for controlling relaxation parameters in subgradient projection methods for convex feasibility problems, providing mathematical guarantees for inconsistent cases and demonstrating computational advantages through numerical experiments.
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm's behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.