Global solution of optimal shape design problems (Q1284531)

Summary: We consider optimal shape design problems defined by pairs of geometrical elements and control functions associated with linear or nonlinear elliptic equations. First, necessary conditions are illustrated in a variational form. Then by applying an embedding process, the problem is extended into a measure-theoretical one, which has some advantages. The theory suggests the development of a computational method consisting of the solution of a finite-dimensional linear programming problem. Nearly optimal shapes and related controls can thus be constructed. Two examples are also given.