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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.
From the book reviews:
"The thesis is well written and organized, structured in three parts: theoretical foundations, numerical methods, and applications and numerical results. The target groups are researches and students in the fields of mathematics, information systems and scientific computing as well as users confronted with PDE constrained optimization problems." (Ctirad Matonoha, zbMATH, Vol. 1293, 2014)
"The thesis is well written and organized, structured in three parts: theoretical foundations, numerical methods, and applications and numerical results. The target groups are researches and students in the fields of mathematics, information systems and scientific computing as well as users confronted with PDE constrained optimization problems." (Ctirad Matonoha, zbMATH, Vol. 1293, 2014)