Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization
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 in matrix and tensor models for which a global Lipschitz-gradient constant need not exist. We show that on an invariant open state-space domain, one iteration of Bregman ADMM defines a smooth primal--dual fixed-point map whose strict-saddle KKT points are unstable fixed points; consequently, from random initialization the iterates converge to a strict saddle with probability zero. Combined with existing first-orde...
| Authors | Shuang Li, Zhihui Zhu, Qiuwei Li |
|---|---|
| Primary category | math.OC |
| Published | 26 June 2026 |
| Last updated at source | 26 June 2026 |
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