Automation in Optimization: Enhancing Decomposition for Proximal and CPU/GPU-Parallel Methods

Optimization practitioners encounter substantial hurdles when transforming and decomposing optimization problems, mainly when these problems comprise diverse components. Some elements may be ideally suited for proximal operators, which excel at managing non-smooth or constrained functions, while others lend themselves to parallel computing, enabling faster computation through distributed workloads. Practitioners must manually determine how to integrate these approaches effectively, demanding deep expertise and considerable time. An automated process could transform this landscape by analyzing problem structures and seamlessly applying the most appropriate techniques to each component. In addition, automation could harness recent advancements in automated parameter selection and acceleration techniques for first-order algorithms, which enhance convergence speed and performance without manual tuning. We introduce an automated system that optimizes computational resources and delivers high-performance solutions, allowing experts to concentrate on strategic tasks like problem formulation and result interpretation.