Stochastic variance-reduced prox-linear algorithms for nonconvex composite optimization

We consider the problem of minimizing composite functions form $$f(g(x))+h(x)$$ , where f and h are convex (which can be nonsmooth) g is a smooth vector mapping. In addition, we assume that average finite number component mappings or expectation over family random mappings. propose class stochastic variance-reduced prox-linear algorithms for solving such problems bound their sample complexities finding an $$\epsilon $$ -stationary point in terms total evaluations Jacobians. When N components, obtain complexity $${\mathcal {O}}(N+ N^{4/5}\epsilon ^{-1})$$ both mapping Jacobian evaluations. general expectation, {O}}(\epsilon ^{-5/2})$$ ^{-3/2})$$ Jacobians respectively. If addition smooth, then improved {O}}(N+N^{1/2}\epsilon derived being respectively,