Convex Approximation Methods for Practical Optimization

Abstract

The method of moving asymptotes (MMA), which is an approach of successive convex approximations, is known to work well for structural optimization problems. The lack of a missing global convergence proof has been closed by the method SCP (sequential convex programming) by adding a line search with respect to the augmented Lagrangian function. The convergence properties will be presented. Traditionally, the subproblems of both versions are solved using a dual approach. In the final stage, many linear systems of the dimension M × M, where M is the number of constraints, have to be solved. These linear systems are dense independent of the structure of the problem. This limits the methods to at most medium sized problems. Now, an interior point approach for the solution of the subproblems is used. The main advantage is, that sparsity properties of the original problem can be preserved for the subproblems, which makes the approach attractive for large scale problems.