Global convergence of trust-region interior-point algorithms for infinite-dimensional nonconvex minimization subject to pointwise bounds

A class of interior-point trust-region algorithms for infinite-dimensional nonlinear optimization subject to pointwise bounds in L^p-Banach spaces, 2≤p≤∞, is formulated and analyzed. The problem formulation is motivated by optimal control problems with L^p-controls and pointwise control constraints. The interior-point trust-region algorithms are generalizations of those recently introduced by Coleman and Li for finite-dimensional problems. Many of the generalizations derived in this paper are also important in the finite-dimensional context. All first- and second-order global convergence results known for trust-region methods in the finite-dimensional setting are extended to the infinite-dimensional framework of this paper.