Extended method of moving asymptotes based on second-order information

The well-known and successful method of moving asymptotes was mainly developedfor 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 withrespect to strict convex approximation of the objective function, deterministicasymptote adaption, and consistent treatment of equality constraints. Itis based on second-order information estimated by forward finite differences.It is shown that the method is identical with diagonal quasi Newton sequentialquadratic programming, if upper and lower asymptotes tend to positive ornegative infinity, respectively. Comparative numerical examples show thesuccess of the proposed extensions for various kinds of nonlinear optimizationproblems.     «

The well-known and successful method of moving asymptotes was mainly developedfor 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 withrespect to strict convex approximation of the objective function, deterministicasymptote adaption, and consistent treatment of equality constraints. Itis based on second-order information estimated...     »