Extended method of moving asymptotes based on second-order information

The well-known and successful method of moving asymptotes was mainly developed for sizing problems in structural optimization. Applied to general problems, e.g. shape optimal design, the method occasionally exhibits some deficiencies. To further generalize the method, a simple extension is presented with respect to strict convex approximation of the objective function, deterministic asymptote adaption, and consistent treatment of equality constraints. It is based on second-order information estimated by forward finite differences. It is shown that the method is identical with diagonal quasi Newton sequential quadratic programming, if upper and lower asymptotes tend to positive or negative infinity, respectively. Comparative numerical examples show the success of the proposed extensions for various kinds of nonlinear optimization problems.