  We consider a non-convex constrained optimization problem, where the
objective function is weakly convex and the constraint function is either
convex or weakly convex. To solve this problem, we consider the classical
switching subgradient method, which is an intuitive and easily implementable
first-order method whose oracle complexity was only known for convex problems.
This paper provides the first analysis on the oracle complexity of the
switching subgradient method for finding a nearly stationary point of
non-convex problems. Our results are derived separately for convex and weakly
convex constraints. Compared to existing approaches, especially the double-loop
methods, the switching gradient method can be applied to non-smooth problems
and achieves the same complexity using only a single loop, which saves the
effort on tuning the number of inner iterations.
