A Further Related Work on Optimization

Different from these gradient-based methods, we focus on the gradient-free methods in this paper. We are also aware of many recent works on the algorithmic design in the structured nonsmooth nonconvex optimization. Then, we proceed to prove the second statement. In this section, we present some technical lemmas for analyzing the convergence property of gradient-free method and its two-phase version. We also give the proofs of Theorem 3.2 and 3.4.