A single loop method for quadratic minmax optimization

What the math gives to ML

The paper converts a coupled constrained convex-concave quadratic saddle problem into one primal-dual residual system and follows its perturbed KKT central path with a single infeasible interior-point loop. Its transferable asset is the simultaneous treatment of primal variables, equality multipliers, and inequality slacks, together with Newton attraction under a nonsingular Jacobian and locally Lipschitz derivatives. A practical neural-network adaptation is a primal-dual optimizer for constrained min-max training, such as robust training with a bounded adversary or resource-constrained mixture-of-experts routing. This is most plausible when the adversarial or routing variables are low-dimensional and projection or alternating gradient updates are unstable.