Wing drag minimization

A shape optimization problem concerned with minimum drag of a thin wing is considered. In this paper, measure theory approach in function space is derived, resulting in an effective algorithm for the discretized optimization problem. First the problem is expressed as an optimal problem governed by variational forms on a fixed domain. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in the measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of the finite-dimensional linear programming problem.