Homogeneous Self-Dual Embedding via Perspective Functions

What the math gives to ML

The paper turns a convex sum minimization problem into a homogeneous primal-dual embedding using perspective functions, so one algorithm can return either a solution or an infeasibility certificate. The transferable asset is the explicit scale variable p: constraints and objectives are represented in a positively homogeneous form, while Douglas-Rachford splitting reduces the resulting iterations to scalar equations and proximity operators. A practical neural-network use is not unconstrained end-to-end training, where nonconvexity invalidates the guarantees, but convex parameter blocks or constrained fine-tuning layers where proximal operators are available and infeasible training specifications should be detected rather than silently optimized.