Inexact-hessian-vector Products for Efficient Reduced-space Pde-constrained Optimization

We investigate reduced-space Newton-Krylov (NK) algorithms for engineering parameter optimization problems constrained by partial-differential equations. We review reduced-space and full-space optimization algorithms, and we show that the efficiency of the reduced-space strategy can be improved significantly with inexact-Hessianvector products computed using approximate second-order adjoints. Results demonstrate that the proposed reduced-space NK algorithm has excellent scaling that makes it suitable for large-scale optimization problems. Moreover, reduced-space NK combines the attractive attributes of both reduced-space quasi-Newton methods and full-space approaches — namely, modularity, robustness, and scalibilty.