On Decomposition Methods for Multidisciplinary Design Optimization

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to certain organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Two natural decomposition approaches to the MDO problem are bilevel decomposition algorithms and Schur interiorpoint methods. Our first contribution is to find a strikingly close relationship between these two approaches. This constitutes one more step towards developing a robust convergence theory for bilevel decomposition algorithms. Our second contribution is to show how Schur interior-point methods can be modified to deal with certain problems for which the Schur complement matrix is not invertible in general. This substantially enlarges the class of problems that can be addressed with this type of methods.