A trust region interior point algorithm for infinite dimensional nonlinear programming

A trust region interior point algorithm for infinite dimensional nonlinear problem, which is motivated by the application of black-box approach to the distributed parameter system optimal control problem with equality and inequality constraints on states and controls, and with bounds on the controls is formulated. By introducing a proper functional which is analogous to the Lagrange function, both equality and inequality constraints can be treated identically and the first order optimality condition is given, then based on the works of Coleman, Ulbrich and Heinkenschloss, the trust region interior point algorithm which is employed to solve the optimization problem under consideration is presented.