A Stochastic Subgradient Method for Nonsmooth Nonconvex Multilevel Composition Optimization

We propose a single time-scale stochastic subgradient method for constrained optimization of composition several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz differentiable in generalized sense. Only estimates the values derivatives used. is parameter-free. prove convergence with probability one method, by associating it system differential inclusions devising nondifferentiable Lyapunov function this system. For problems having continuous derivatives, finds point satisfying an optimality measure error order $1/\sqrt{N}$, after executing $N$ iterations constant stepsize.