@INPROCEEDINGS{Akcelic02, AUTHOR = {Volkan Akcelik and George Biros and Omar Ghattas}, TITLE = {Parallel Multiscale Gauss-Newton-Krylov Methods for Inverse Wave Propagation}, BOOKTITLE = {Proceedings of SC2002}, YEAR = {2002}, ADDRESS = {Baltimore}, MONTH = {November}, ORGANIZATION = {IEEE/ACM}, PDF = {http://www.cs.cmu.edu/~oghattas/papers/sc2002.pdf}, ABSTRACT = {One of the outstanding challenges of computational science and engineering is large-scale parameter estimation of systems governed by partial differential equations. These are known as inverse problems, in contradistinction to the forward problems that usually characterize large-scale simulation. Inverse problems are significantly more difficult to solve than forward problems, due to ill-posedness, large dense ill-conditioned operators, multiple minima, space-time coupling, and the need to solve the forward problem repeatedly. We present a parallel algorithm for inverse problems governed by time-dependent PDEs, and scalability results for an application in inverse heterogeneous wave propagation. The difficulties mentioned above are addressed through a combination of total variation regularization, preconditioned matrix-free Gauss-Newton-Krylov iteration, checkpointing, and multiscale continuation. We are able to solve an inverse problem of wave propagation though a pelvic bone structure involving two million inversion parameters in 3 hours on 256 processors of the Terascale Computing System at the Pittsburgh Supercomputing Center. }, NOTE = {SC2002 Best Technical Paper Award} } @ARTICLE{AkcelikBirosGhattasLongVanBloemenWaanders2003, AUTHOR = {Akcelik V. and Biros G. and Ghattas O. and Long K. and van Bloemen Waanders B.}, TITLE = {A variational finite element method for source inversion of contaminant transport processes}, JOURNAL = {Finite Elements in Analysis and Design}, VOLUME = {39}, PAGES = {683--705}, MONTH = {May}, YEAR = {2003} } @TECHREPORT{SSCollis_MHeinkenschloss_2002a, AUTHOR = {S. S. Collis and M. Heinkenschloss}, TITLE = {{Analysis of the Streamline Upwind/Petrov Galerkin Method Applied to the Solution of Optimal Control Problems}}, INSTITUTION = {Department of Computational and Applied Mathematics}, ADDRESS = {Rice University, Houston, TX 77005--1892}, NUMBER = {TR02--01}, YEAR = {2002}, URL = {http://www.caam.rice.edu/~heinken}, ABSTRACT = {We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the numerical solution of such optimal control problems. In the discretize-then-optimize approach the optimal control problem is first discretized, using the SUPG method for the discretization of the advection-diffusion equation, and then the resulting finite dimensional optimization problem is solved. In the optimize-then-discretize approach one first computes the infinite dimensional optimality system, involving the advection-diffusion equation as well as the adjoint advection-diffusion equation, and then discretizes this optimality system using the SUPG method for both the original and the adjoint equations. These approaches lead to different results. The main result of this paper are estimates for the error between the solution of the infinite dimensional optimal control problem and their approximations computed using the previous approaches. For a class of problems prove that the optimize-then-discretize approach has better asymptotic convergence properties if finite elements of order greater than one are used. For linear finite elements our theoretical convergence results for both approaches are comparable, except in the zero diffusion limit where again the optimize-then-discretize approach seems favorable. Numerical examples are presented to illustrate some of the theoretical results.} } @INPROCEEDINGS{Young-PDE-02, AUTHOR = {D. P. Young and W. P. Huffman and R. G. Melvin and C. L. Hilmes and F. T. Johnson}, TITLE = {Nonlinear Elimination in Aerodynamic Analysis and Design Optimization}, BOOKTITLE = {Proceedings of the First Sandia Workshop on Large-Scale PDE Constrained Optimization (to appear)}, YEAR = {2002}, SERIES = {Lecture Notes in Computational Science and Engineering}, PUBLISHER = {Springer Verlag}, PS = {young-lnsce.ps.gz}, PDF = {young-lnsce.pdf}, ABSTRACT = { Recent emphasis on reduction of design cycle time and cost in the design of commercial aircraft has sparked a renewed interest in design optimization in aerodynamics, structures, and aeroelastics. The constrained aerodynamic optimization problem is closely related to the problem of solving nonlinear systems of equations. In applying Newton's method to steady-state compressible CFD analysis problems, the nonlinear elimination method has been remarkably successful. In this paper we consider the implications of this experience for design optimization formulations in the general case of state equation equality constraints. This relationship between nonlinear equation solving and design optimization is illustrated by drawing on computational examples from the TRANAIR compressible CFD code. We first discuss various formulations of the PDE constrained optimization problem related to the Lagrange Newton method and the multiplier free version implementation in TRANAIR. We then discuss the nonlinear elimination method and its application to a simple nozzle problem. This method is then applied to derive various globalization methods in design optimization which are illustrated by a computational example in airfoil design. Finally, we discuss some remaining limitations and issues.} } @TECHREPORT{abraham1, AUTHOR = {F. Abraham and M. Behr and M. Heinkenschloss}, TITLE = {The effect of stabilization on the optimal control of the {Oseen} equations (submitted for publication)}, INSTITUTION = {Department of Computational and Applied Mathematics, Rice University}, NUMBER = {CAAM TR03-04}, YEAR = {2003} } @ARTICLE{barlett1, AUTHOR = {Bartlett, R. A. and L. T. Biegler}, TITLE = {QPSchur: A Dual, Active Set, {Schur} Complement Method for Large-scale and Structured Convex Quadratic Programming Algorithm}, JOURNAL = {submitted for publication}, YEAR = {2002} } @INPROCEEDINGS{bart1, AUTHOR = {van Bloemen Waanders, Bart and Roscoe Bartlett and Lorenz T. Biegler and Carl D. Laird}, TITLE = {Nonlinear Programming Strategies for Source Detection of Municipal Water Networks}, BOOKTITLE = {Proceedings EWRI Conference} } @BOOK{biegler2, AUTHOR = {L. Biegler and O. Ghattas and M. Heinkenschloss and B. van Bloemen Waanders}, TITLE = {Large-scale {PDE}-constrained Optimization}, SERIES = {Lecture Notes in Computational Science and Engineering}, PUBLISHER = {Springer Verlag}, VOLUME = {30}, YEAR = {2003} } @INCOLLECTION{biegler3, AUTHOR = { L. T. Biegler and Andreas Waechter}, TITLE = {{SQP SAND} Strategies that Link to Existing Modeling Systems}, SERIES = {Lecture Notes in Computational Science and Engineering}, VOLUME = {30}, PUBLISHER = {Springer-Verlag}, YEAR = {2003}, EDITOR = {Ghattas, Heinkenschloss, Biegler and van Bloemen Waanders}, BOOKTITLE = {Large-Scale PDE Constrained Optimization} } @ARTICLE{biros1, AUTHOR = {G. Biros and O. Ghattas}, TITLE = {{Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part I: The Krylov-Schur Solver}}, JOURNAL = {SIAM Journal on Scientific Computing (submitted)}, YEAR = {2000} } @ARTICLE{biros2, AUTHOR = {G. Biros and O. Ghattas}, TITLE = {{Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange-Newton Solver, and its Application to Optimal Control of Steady Viscous Flows}}, JOURNAL = {SIAM Journal on Scientific Computing (submitted)}, YEAR = {2000} } @INCOLLECTION{biros3, AUTHOR = {G. Biros and O. Ghattas}, TITLE = {Inexactness Issues in the {Lagrange-Newton-Krylov-Schur} method}, SERIES = {Lecture Notes in Computational Science and Engineering}, VOLUME = {30}, PUBLISHER = {Springer-Verlag}, YEAR = {2003}, EDITOR = {Ghattas, Heinkenschloss, Biegler and van Bloemen Waanders}, BOOKTITLE = {Large-Scale PDE Constrained Optimization} } @ARTICLE{cai1, AUTHOR = {X.-C. Cai and D. E. Keyes}, TITLE = {Nonlinearly Preconditioned Inexact {Newton} Algorithms}, JOURNAL = {SIAM J. Sci. Comp}, YEAR = {2002}, VOLUME = {24}, PAGES = {183--200} } @ARTICLE{itle1, AUTHOR = {Itle, G. C. and A. G. Salinger and R. P. Pawlowski and J.N. Shadid and L. T. Biegler}, TITLE = {A Tailored Optimization Strategy for {PDE}-based Design: Application to a {CVD} Reactor}, JOURNAL = {submitted for publication}, YEAR = {2002} } @MASTERSTHESIS{jannet, AUTHOR = { J. Berschling}, TITLE = {Inverse problems in multiphase groundwater flow}, SCHOOL = { Department of Civil and Environmental Engineering, Carnegie Mellon University}, YEAR = {2003} } @ARTICLE{jock1, AUTHOR = {Jockenhoevel, T. and L. T. Biegler and A. Waechter}, TITLE = {Dynamic Optimization of the Tennessee Eastman Process Using the OptControlCentre}, JOURNAL = {Computers and Chemical Engineering}, YEAR = {2003}, VOLUME = {27}, NUMBER = {11}, PAGES = {1513--1531} } @ARTICLE{keyes-jcp-04, AUTHOR = {D.A. Knoll and D.E. Keyes}, TITLE = {Jacobian-free {Newton--Krylov} methods: a Survey of approaches and applications}, JOURNAL = {Journal of Computational Physics}, YEAR = {2004}, VOLUME = {193}, PAGES = {357--397} } @INCOLLECTION{keyes3, AUTHOR = {D. E. Keyes and P. D. Hovland and L. C. McInnes and W. Samyono}, TITLE = {Using Automatic Differentiation for Second-order Matrix-free Methods in {PDE}-constrained Optimization}, PUBLISHER = {Springer Verlag}, YEAR = {2002}, EDITOR = {G. Corliss et al}, BOOKTITLE = {Automatic Differentiation of Algorithms: From Simulation to Optimization} } @MASTERSTHESIS{mallet, AUTHOR = { V. Mallet}, TITLE = {Simulation numerique de la propagation d'interfaces}, SCHOOL = {Ecole Centrale de Lyon}, YEAR = {2002} } @ARTICLE{raghu1, AUTHOR = {Raghunathan, A. and L. T. Biegler}, TITLE = {MPEC Formulations and Algorithms in Process Engineering}, JOURNAL = {Computers and Chemical Engineering}, YEAR = {2003}, TVOLUME = {27}, PAGES = {1381--1392} } @INCOLLECTION{roscoe1, AUTHOR = { Roscoe A. Bartlett and Lorenz T. Biegler}, TITLE = {{rSQP++} : An Object-Oriented Framework for Successive Quadratic Programming}, SERIES = {Lecture Notes in Computational Science and Engineering}, VOLUME = {30}, PUBLISHER = {Springer-Verlag}, YEAR = {2003}, EDITOR = {Ghattas, Heinkenschloss, Biegler and van Bloemen Waanders}, BOOKTITLE = {Large-Scale PDE Constrained Optimization} } @INCOLLECTION{salinger1, AUTHOR = {A.G. Salinger and R.P. Pawlowski and J.N. Shadid and B.van Bloemen Waanders and R. Bartlett and G.C. Itle and L. Biegler}, TITLE = {{rSQP} Optimization of Large-Scale Reacting Flow Applications with {MPSalsa}}, SERIES = {Lecture Notes in Computational Science and Engineering}, PUBLISHER = {Springer-Verlag}, VOLUME = {30}, YEAR = {2003}, EDITOR = {L. Biegler and O. Ghattas and M. Heinkenschloss and B. van Bloemen Waanders}, BOOKTITLE = {Large-Scale PDE-Constrained Optimization} } @ARTICLE{santos1, AUTHOR = {Santos, L.O. and L. T. Biegler}, TITLE = {A Tool to Analyze Robust Stability for constrained Model Predictive Controllers}, JOURNAL = {ADCHEM 2003}, YEAR = {2003} } @INPROCEEDINGS{sc2003, AUTHOR = {Volkan Akcelik and Jacobo Bielak and George Biros and Ioannis Epanomeritakis and Antonio Fernandez and Omar Ghattas and Eui Joong Kim and Julio Lopez and David O'Hallaron and Tiankai Tu and John Urbanic}, TITLE = {High Resolution Forward and Inverse Earthquake Modeling on Terascale Computers}, BOOKTITLE = {Proceedings of SC2003}, PUBLISHER = {ACM/IEEE}, ADDRESS = {Phoenix}, YEAR = 2003 } @ARTICLE{waechter1, AUTHOR = {Waechter, A. and L. T. Biegler}, TITLE = {Global and Local Convergence of Line Search Filter Methods for Nonlinear Programming}, JOURNAL = {submitted for publication}, YEAR = {2001} }