Optimality Condition for Infinite-dimensional Programming Problem with Operator and Bound Constraints

Abstract:

      A first-order necessary condition for an infinite-dimensional nonlinear op- timization problem, which arises when the all-at-once method is employed to slove the optimal control problems, is formulated and analyzed. Operator constraint and simple bound on part of the variables are both considered. Based on this optimality condition, the trust-region subproblems are built, then the trust region method rnay be employed to deal with the optimizatiou problem in infinite-dimensional space.