Exploring the Method of Moving Asymptotes for Various Optimization Applications

Abstract

The development of sequential explicit, convex approximation schemes has allowed for expansion of the size of optimization problems that can now be achieved. These approximation schemes use information from the original optimization statement to generate a series of approximate subproblems allowing for an efficient solution strategy. This thesis reviews established sequential explicit, convex approximations in the literature along with a brief overview of their associated solution schemes. A primary focus is placed on the theory and application of the Method of Moving Asymptotes (MMA) approximation due to its continued regard in the field of structural topology optimization. Numerical examples explore optimization problems solved by the MMA approximation in order to demonstrate the behavior of this method and impact of the prescribed empirical parameters. Other numerical examples study structural topology optimization problems in the 2D and 3D setting to compare with alternative, competitive update schemes such as the OC and to highlight the benefit of using the MMA in more complex settings.M.S