Large-Scale Nonlinear Programming for Multi-scenario Optimization

Multi-scenario optimization is a convenient way to formulate design optimization problems that are tolerant to disturbances and model uncertainties and/or need to operate under a variety of different conditions. Moreover, this problem class is often an essential tool to deal with semi-infinite problems. Here we adapt the IPOPT barrier nonlinear programming algorithm to provide efficient parallel solution of multi-scenario problems. The recently developed object oriented software, IPOPT 3.1, has been specifically designed to allow specialized linear algebra in order to exploit problem specific structure. Here, we discuss the high level design principles of IPOPT 3.1 and develop a parallel Schur complement decomposition approach for large-scale multi-scenario optimization problems. A large-scale example for contaminant source inversion in municipal water distribution systems is used to demonstrate the effectiveness of this approach, and parallel results with up to 32 processors are shown for an optimization problem with over a million variables.