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Mathematics | Optimization with PDE Constraints

Optimization with PDE Constraints

Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.

2009, XII, 270 p.

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  • Concise functional analytic setting for pde constrained optimization problems
  • Modern infinite-dimensional tailored algorithmical framework
  • Structure exploiting, problem adapted discrete treatment of pdes and constraints
  • Challenging applications

This book presents a modern introduction of pde constrained optimization. It provides a precise functional analytic treatment via optimality conditions and a state-of-the-art, non-smooth algorithmical framework. Furthermore, new structure-exploiting discrete concepts and large scale, practically relevant applications are presented. The main focus is on the algorithmical and numerical treatment of pde constrained optimization problems on the infinite dimensional level. A particular emphasis is on simple constraints, such as pointwise bounds on controls and states. For these practically important situations, tailored Newton- and SQP-type solution algorithms are proposed and a general convergence framework is developed. This is complemented with the numerical analysis of structure-preserving Galerkin schemes for optimization problems with elliptic and parabolic equations. Finally, along with the optimization of semiconductor devices and the optimization of glass cooling processes, two challenging applications of pde constrained optimization are presented. They demonstrate the scope of this emerging research field for future engineering applications.

Content Level » Research

Keywords » Applications - Banach spaces - Optimal control - Optimality theory - PDE constrained optimization - Tailored discrete concepts - numerical analysis

Related subjects » Analysis - Computational Science & Engineering - Mathematics

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