Editing Shape optimization (section)

{{Short description|Problem of finding the optimal shape under given conditions}}
{{More footnotes|date=June 2020}}

'''Shape optimization''' is part of the field of [[optimal control]] theory. The typical problem is to find the [[shape]] which is optimal in that it minimizes a certain cost [[functional (mathematics)|functional]] while satisfying given [[constraint (mathematics)|constraints]]. In many cases, the functional being solved depends on the solution of a given [[partial differential equation]] defined on the variable domain.

[[Topology optimization]] is, in addition, concerned with the number of connected components/boundaries belonging to the domain. Such methods are needed since typically shape optimization methods work in a subset of allowable shapes which have fixed topological properties, such as having a fixed number of holes in them. Topological optimization techniques can then help work around the limitations of pure shape optimization.