A modification of convex approximation methods for structural optimization

The most popular convex approximation methods used today in structural optimization are discussed in this paper: the convex linearization method (CONLIN), the method of the moving asymptotes (MMA) and the sequential quadratic programming method (SQP). Modifications are made to enhance the reliability of the CONLIN method. In addition, a generalized MMA (GMMA) is established. However, in view of practical difficulties of evaluating second-order derivatives, a fitting scheme is proposed in this work to adjust the convexity of the approximation based on the available function value at the preceding design iteration. Numerical results show that this simple scheme is efficient in our applications.