A stochastic gradient method for a class of nonlinear PDE-constrained optimal control problems under uncertainty

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class optimization is strongly utilized engineering, biology and finance. In this paper, a stochastic gradient method proposed for the resolution nonconvex problem on Hilbert space. We show that, suitable assumptions, strong or weak accumulation points iterates produced by converge almost surely to stationary original problem. Measurability convergence rates stationarity measure are handled, filling gap applications infinite dimensional problems. demonstrated constrained elliptic semilinear partial differential equations (PDEs) uncertainty.