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.

[1]  Robert J. Vanderbei,et al.  Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions , 2002, Comput. Optim. Appl..

[2]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[3]  John T. Betts,et al.  Large Scale Parameter Estimation Using Sparse Nonlinear Programming Methods , 2003, SIAM J. Optim..

[4]  L. Biegler,et al.  Multiperiod design and planning with interior point methods , 1999 .

[5]  Günter Wozny,et al.  Sequential Parameter Estimation for Large-Scale Systems with Multiple Data Sets. 1. Computational Framework , 2003 .

[6]  U. Ascher,et al.  A New Basis Implementation for a Mixed Order Boundary Value ODE Solver , 1987 .

[7]  In Sun Kim,et al.  Recent advances in polymer reaction engineering: Modeling and control of polymer properties , 2004 .

[8]  Hans Seidl,et al.  Peroxides as Initiators for High-Pressure Polymerization , 1981 .

[9]  C. Kiparissides,et al.  On‐line parameter estimation in a high‐pressure low‐density polyethylene tubular reactor , 1996 .

[10]  J. Macgregor,et al.  Mathematical Modeling, Optimization, and Quality Control of High-Pressure Ethylene Polymerization Reactors , 1993 .

[11]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[12]  P. Moran.  Estimating structural and functional relationships , 1971 .

[13]  W. Harmon Ray,et al.  On the Mathematical Modeling of Polymerization Reactors , 1972 .

[14]  L. Biegler,et al.  Advances in simultaneous strategies for dynamic process optimization , 2002 .

[15]  Ignacio E. Grossmann,et al.  Retrospective on optimization , 2004, Comput. Chem. Eng..

[16]  D. K. Varvarezos,et al.  Multiperiod design optimization with SQP decomposition , 1994 .

[17]  M. B. Kelly,et al.  Mathematical Modeling of Free-Radical Ethylene Copolymerization in High-Pressure Tubular Reactors , 2005 .

[18]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[19]  Jacek Gondzio,et al.  Exploiting structure in parallel implementation of interior point methods for optimization , 2009, Comput. Manag. Sci..

[20]  G. Luft,et al.  Effectiveness of Organic Peroxide Initiators in the High-Pressure Polymerization of Ethylene , 1977 .

[21]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[22]  L. Biegler,et al.  Large-Scale Parameter Estimation in Low-Density Polyethylene Tubular Reactors , 2006 .

[23]  T. Edgar,et al.  A sequential error-in-variables method for nonlinear dynamic systems , 1991 .

[24]  J. Gondzio,et al.  Solving Nonlinear Financial Planning ProblemsWith 109 Decision Variables On MassivelyParallel Architectures , 2006 .

[25]  W. E. Stewart,et al.  Sensitivity analysis of initial value problems with mixed odes and algebraic equations , 1985 .

[26]  George Biros,et al.  Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part I: The Krylov-Schur Solver , 2005, SIAM J. Sci. Comput..

[27]  A. Buchelli,et al.  Modeling Fouling Effects in LDPE Tubular Polymerization Reactors. 2. Heat Transfer, Computational Fluid Dynamics, and Phase Equilibria , 2005 .