Recent advances in convex approximation methods for structural optimization

The most popular convex approximation methods used today in structural optimization are studied in this paper: the CONvex LINearization method (CONLIN), the Method of the Moving Asymptotes (MMA) and the Sequential Quadratic Programming method (SQP). It is shown that the convexity is the basic factor of great importance to ensure the approximation quality, especially the feasibility of intermediate solutions in the design cycle. In view of the practical difficulties of computing second order derivatives, a fitting scheme is proposed, which allows to adjust automatically the convexity of the approximation based on the available function value at the preceding design iteration. Results of numerical examples show that this simple scheme is efficient in our applications.