For FE-based structural optimiza.tion systems, a. large variety of different numerical algorithms ia ava.i\able, e.g. sequential linear programming, sequential quadratic programming, convex approximation, generalized reduced gradient, multiplier, penalty or optimality criteria. methods, and combina.tions of these approaches. The purpose of the pa.per is to present the numerical reaults of a comparative study of eleven rnathematical programrning codes which represent typical realizations of the mathema.tical methods mentioned. They a.re implemented in the structural optimization system MBB-LAGRANGE, which proceeds from a typical finite element analysis. The comparative results are obtained from a collection of79 test problems. The majority ofthem are academic test cases, the others possess some practical reßlliJe background. Optirnization is performed with respect to sizing of trusses and bearns, wall thicknesses, etc., subject to stress, displacement, and many other constraints. Numerical cornparison is based on reliability and efficiency measured by calculation time ana number of analyses needed to reach a certain accura.cy level.

The method of moving asymptotes (MMA) which is known to work excellently for solving structural optimization problems has one main disadvantage: convergence cannot be guaranteed and in practical use this fact sometimes leads to unsatisfactory results. In this paper we prove agIobaI convergence theorem {m a new method which consists iteratively of the solution of thc known MMA-subproblem and a line search'performed afterwards.

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Dedicated to Professor Jochem ZoweWe introduce a method for constrained nonlinear programming that is widely used in mechanical engineering and that is known under the name SCP for sequential convex programming. The algorithm consists of solving a sequence of convex and separable subproblems, where an augmented Lagrangian merit function is used for guaranteeing convergence. Originally, SCP methods were developed in structural mechanical optimization, and are particularly applied to solve topology optimization problems. These problems are extremely large and possess dense Hessians of the objective function. The purpose of the article is to show that constrained dense nonlinear programs with 10 5 -10 6 variables can be solved successfully and that SCP methods can be applied also to optimal control problems based on semilinear elliptic partial differential equations after a full discretization.

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