Shape optimization

Shape optimization is a branch of optimization, which is concerned with finding an optimal shape, or even an optimal topology of a shape, given an objective function, and possibly constraints. That is, the aim to find a bounded set D, minimzing a functional

${\mathcal {F}}(D)$,

possibly subject to a constrant of the form

${\mathcal {G}}(D)=0.$

The set D is required to have Lipschitz or C¹ boundary.

Shape optimization is an infinte dimensional optimization problem.