Best Minimizing Algorithm for Shape-measure Method

The Shape-Measure method for solving optimal shape design problems (OSD) in cartesian coordinates is divided into two steps. First, for a fixed shape (domain), the problem is transferred to the space of positive Radon measures and relaxed to a linear programming in which its optimal coefficients determine the optimal pair of trajectory and control. Then, a standard minimizing algorithm is used to identify the best shape. Here we deal with the best standard algorithm to identify the optimal solution for an OSD sample problem governed by an elliptic boundary control problem.