Optimization with PDE Constraints

Optimization problems in which a partial differential equation serves as the constraint are the subject here. The treatment works at the infinite-dimensional level, relying on functional analysis to establish the conditions a solution must satisfy.

A central concern is how to solve these problems algorithmically and numerically. Simple restrictions, such as pointwise limits on controls and states, receive special attention. For this setting the author develops Newton-type and SQP-type methods, alongside a general framework that establishes their convergence. The discussion also covers structure-preserving Galerkin schemes for elliptic and parabolic equations, and discrete approaches that exploit problem structure at large scale.

The closing chapters apply these methods to two demanding cases: the optimization of semiconductor devices and the optimization of glass cooling processes. Together they illustrate how the approach can be used in engineering practice.