Introduction

Abstract

The idea to use the implicit programming approach in optimum shape design problems is in fact quite old. It was extensively used for solving problems with equilibrium constraints given by variational equations. In this case it is straightforward to plug the unique solution of the equation into the objective function and compute derivatives of such a composite function by means of the implicit-function theorem. If the equilibrium problem is more complicated, e.g., it is a variational inequality, this technique becomes less straightforward. In classic shape optimization, one circumvents the difficulty (switch from equality to inequality) by means of the regularization technique.