Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems

Multi-scenario optimization is a convenient way to formulate and solve multi-set parameter estimation problems that arise from errors-in-variables-measured (EVM) formulations. These large-scale problems lead to nonlinear programs (NLPs) with specialized structure that can be exploited by the NLP solver in order to obtained more efficient solutions. Here we adapt the IPOPT barrier nonlinear programming algorithm to provide efficient parallel solution of multi-scenario problems. The recently developed object oriented framework, IPOPT 3.2, has been specifically designed to allow specialized linear algebra in order to exploit problem specific structure. This study discusses high-level design principles of IPOPT 3.2 and develops a parallel Schur complement decomposition approach for large-scale multi-scenario optimization problems. A large-scale case study example for the identification of an industrial low-density polyethylene (LDPE) reactor model is presented. The effectiveness of the approach is demonstrated through the solution of parameter estimation problems with over 4100 ordinary differential equations, 16,000 algebraic equations and 2100 degrees of freedom in a distributed cluster.