|Abstract:|| We examine shape optimization problems in the context of inexact sequential
quadratic programming. Inexactness is a consequence of using adaptive
finite element methods (AFEM) to approximate the state
and adjoint equations (via the dual weighted residual method),
update the boundary, and compute the geometric functional.
We present a novel algorithm that equidistributes the errors due to
shape optimization and discretization, thereby leading to
coarse resolution in the early stages and fine resolution upon
convergence, and thus optimizing the computational effort.
We discuss the ability of the algorithm
to detect whether or not geometric singularities such as corners are
genuine to the problem
or simply due to lack of resolution---a new paradigm in adaptivity.