Adaptive SQP Method for Shape Optimization

Abstract

We examine shape optimization problems in the context of inexact sequential quadratic program- ming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state equation, update the boundary, and compute the geometric functional. We present a novel algorithm that uses a dynamic tolerance and equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence. 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