This volume provides a broad and uniform introduction of PDE-constrained optimization as well
as to document a number of interesting and challenging applications. Many science and
engineering applications necessitate the solution of optimization problems constrained by
physical laws that are described by systems of partial differential equations (PDEs) . As a
result PDE-constrained optimization problems arise in a variety of disciplines including
geophysics earth and climate science material science chemical and mechanical engineering
medical imaging and physics. This volume is divided into two parts. The first part provides a
comprehensive treatment of PDE-constrained optimization including discussions of problems
constrained by PDEs with uncertain inputs and problems constrained by variational inequalities.
Special emphasis is placed on algorithm development and numerical computation. In addition a
comprehensive treatment of inverse problems arising in the oil and gas industry is provided.
The second part of this volume focuses on the application of PDE-constrained optimization
including problems in optimal control optimal design and inverse problems among other
topics.
