Dual quasi-Newton method in Hilbert spaces with an application to state-constrained optimal control problems

Quasi-Newton methods are extended to optimization problems with an operator constraint in Hilbert spaces. In these algorithms, quadratic programming subproblems with a set constraint are iteratively solved to obtain estimates of Lagrange multipliers, and a sequence of search directions is generated with these estimates. These methods are then applied to optimal control problems with state inequality constraints. In this case, the control problem is reduced to a series of nonnegatively constrained quadratic programming problems in a function space and they can be easily solved, e.g., by clipping-off techniques. A numerical example is also presented to illustrate the usefulness of the proposed algorithm. [In Japanese.]