2020/01/29 by Ruszczynski, Andrzej
#49J52 #62L20 #90C15 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2001.10669
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized sense. Only stochastic estimates of the values and generalized derivatives of the functions are used. The method is parameter-free. We prove convergence with probability one of the method, by associating with it a system of differential inclusions and devising a nondifferentiable Lyapunov function for this system. For problems with functions having Lipschitz continuous derivatives, the method finds a point satisfying an optimality measure with error of order 1/√(N), after executing N iterations with constant stepsize.