Line search globalization of a semismooth Newton method for operator equations in Hilbert spaces with applications in optimal control

摘要: We consider the numerical solution of nonlinear and nonsmooth operator equations in Hilbert spaces. A semismooth Newton method is used for search direction generation. The equation solved by a globalized that equipped with an Armijo linesearch using merit function. prove accumulation point algorithm transition to fast local convergence under directional Hadamard-like continuity assumption on matrix. In particular, no auxiliary descent directions or smoothing steps are required. Finally, we apply this control-constrained also regularized state-constrained optimal control problem subject partial differential equations.