Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization

Analyzing Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness matters because the condition replaces the standard Lipschitz gradient assumption with Hessian comparison relative to a Bregman kernel.

We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a Hessian comparison relative to a Bregman kernel. This setting covers polynomial objectives arising…