A Moving Ball Projection Algorithm for the Split Feasibility Problem

We address the split feasibility problem with convex sublevel sets that are computationally expensive to project onto. Instead of conventional half-space approximations, we introduce a moving ball projection method based on a sequence of closed balls inside the sublevel sets. These projections are computationally efficient and admit closed-form solutions. Moreover, the method preserves feasibility at every iterate, promoting faster convergence. We establish global convergence under mild assumptions and demonstrate the algorithm's effectiveness through numerical examples. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.