## Modeling Truss Structures using Vanishing and Cardinality Constraints

### Alexandra Schwartz, Anne Tabbert

When constructing a truss one can try to optimize its geometry with respect to certain objectives such as total weight. On the other hand, to ensure its stability under load, stress constraints have to be satisfied for those bars, which are realized in the optimal design. This can be modeled using vanishing constraints, see e.g. Achtziger, Kanzow 2008. However, the resulting designs often contain many thin bars, which may be due to numerical inaccuracies and is not practical to realize.

For this reason, we consider an extended formulation of the optimization problem with an additional cardinality constraint, which limits the number of bars that may be realized. We analyze the structure of the resulting optimization problem with vanishing and cardinality constraints with respect to necessary optimality conditions and suggest an adapted relaxation method. Numerical results for academic examples are presented.