Curvature Recycling Douglas-Rachford Splitting: Transported Quasi-Newton Models for Expensive Smooth Proximal Subproblems

What the math gives to ML

The paper introduces a practical way to reuse curvature across a sequence of related smooth proximal subproblems instead of restarting an inner optimizer at every Douglas–Rachford iteration. The transferable asset is the exact residual-transport identity: changing only the quadratic proximal center shifts the optimality residual by a known vector, allowing an old proximal state and quasi-Newton model to be reused before evaluating a new expensive gradient. This is relevant to composite neural objectives with expensive differentiable losses and cheap proximal regularizers such as group sparsity, pruning, or structured parameter constraints. A safeguarded limited-memory implementation is the most direct first experiment.