A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions (defined in matrix variables) are approximated by block-separable convex functions. The subproblems are semidefinite programs with a favorable structure, which can be efficiently solved by existing SDP software. The new method is shown to be globally convergent. The article is concluded by a series of numerical experiments demonstrating the effectiveness of the generalized SCP approach.
Preprint 317, Institute of Applied Mathematics, University of Erlangen-Nuremberg, 2007