A Direct Method for Parabolic PDE Constrained Optimization Problems



A Direct Method for Parabolic PDE Constrained Optimization Problems
Andreas Potschka discusses a direct multiple shooting method for dynamic optimization problems constrained by nonlinear, possibly time-periodic, parabolic partial differential equations. In contrast to indirect methods, this approach automatically computes adjoint derivatives without requiring the user to formulate adjoint equations, which can be time-consuming and error-prone. The author describes and analyzes in detail a globalized inexact Sequential Quadratic Programming method that exploits the mathematical structures of this approach and problem class for fast numerical performance. The book features applications, including results for a real-world chemical engineering separation problem.
Contents
· Parabolic PDE Constrained Optimization Problems
· Two-Grid Newton-Picard Inexact SQP
· Structure Exploiting Solution of QPs
· Applications and Numerical Results
Target Groups
· Researchers and students in the fields of mathematics, information systems, and scientific computing
· Users with PDE constrained optimization problems, in particular in (bio-)chemical engineering
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