Zhihui Zhu

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

It is shown 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, which yields almost-sure second-order stationarity of limiting KKT points.