Interior-point methods for PDE-constrained optimization

Autor*innen

• Johannes Huber

Parameter

• Lehrbücher
• Universitätslehrbücher

Mehr zum Buch

In applied sciences, PDEs model a wide range of phenomena, often aiming for an optimal system in simulations. These PDE-constrained optimization problems are typically large-scale and nonconvex, leading to ill-conditioned linear systems. Inequality constraints often reflect technical limitations or prior knowledge. This thesis explores interior-point (IP) methods for solving nonconvex large-scale PDE-constrained optimization problems with such constraints. To address the challenges posed by direct linear solvers, inexact search directions are incorporated into an inexact IP method. SMART tests help manage the lack of inertia information, controlling Hessian modification and defining termination tests for the iterative linear solver. The original inexact IP method requires solving two sparse large-scale linear systems per optimization step, which is optimized to a single system solution in most steps. Two iterative linear solvers are evaluated: a general-purpose algebraic multilevel preconditioned SQMR method applied to optimal server room cooling and ambient temperature computation, demonstrating robustness and efficiency compared to the exact IP method. The RSP GMRES solver, leveraging the linear system's structure, is also analyzed for control problems in superconductivity and groundwater modeling, showing improved efficiency, especially with multiple PDE constraints. The thesis further addresses an inverse medium problem fo

• Sprache: Englisch
• Erscheinungsdatum: 2013