Avoiding strict saddle points of nonconvex regularized problems
Luwei Bai
We introduce a strict saddle property for $\ell_p$ regularized functions, and
propose an iterative reweighted $\ell_1$ algorithm to solve the $\ell_p$
regularized problems. The algorithm is guaranteed to converge only to local
minimizers when randomly initialized. The strict saddle property is shown
generic on these sparse optimization problems. Those analyses as well as the
proposed algorithm can be easily extended to general nonconvex regularized
problems.