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

SIAM Journal on Scientific Computing

Volumn 27, Issue 2, 2006, Pages 714-739

  Biros, George ^a   Ghattas, Omar ^b  

^a NEW YORK UNIVERSITY   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Adjoint methods; Finite elements; Indefinite systems; Lagrange Newton Krylov Schur methods; Navier Stokes; Nonlinear equations; Optimal control; Parallel algorithms; PDE constrained optimization; Preconditioners; Sequential quadratic programming

Indexed keywords

CONSTRAINT THEORY; ITERATIVE METHODS; NONLINEAR EQUATIONS; OPTIMIZATION; PARALLEL ALGORITHMS; QUADRATIC PROGRAMMING; VISCOUS FLOW;

ADJOINT METHODS; FINITE ELEMENTS; INDEFINITE SYSTEMS; LAGRANGE-NEWTON-KRYLOV-SCHUR METHODS; NAVIER-STOKES; OPTIMAL CONTROL; PDE-CONSTRAINED OPTIMIZATION; PRECONDITIONERS; SEQUENTIAL QUADRATIC PROGRAMMING;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33644965417     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502415661     Document Type: Article

References (25)

1. E. L. ALLGOWER AND K. GEORG, Introduction to Numerical Continuation Methods, SIAM, Philadelphia, 2003.
2. I. BABUŠKA, The finite element method with Lagrangian multipliers, Numer. Math., 20 (1973), pp. 179-192.
3. G. BIROS AND O. GHATTAS, Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part I: The Krylov-Schur solver, SIAM J. Sci. Comput., 27 (2005), pp. 687-713.
4. P. T. BOGGS AND J. W. TOLLE, A strategy for global convergence in a sequential quadratic programming algorithm, SIAM J. Numer. Anal., 26 (1989), pp. 600-623.
5. J. E. DENNIS, JR., M. EL-ALEM, AND M. C. MACIEL, A global convergence theory for general trust-region-based algorithms for equality constrained optimization, SIAM J. Optim., 7 (1997), pp. 177-207.
6. S. C. EISENSTAT AND H. F. WALKER, Globally convergent inexact Newton methods, SIAM J. Optim., 4 (1994), pp. 393-422.
7. S. C. EISENSTAT AND H. F. WALKER, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), pp. 16-32.
8. R. FLETCHER, Practical Methods of Optimization, 2nd ed., John Wiley and Sons, Chichester, UK, 1987.
9. P. E. GILL, W. MURRAY, AND M. H. WRIGHT, Practical Optimization, Academic Press, London, New York, 1981.
10. M. D. GUNZBURGER, Finite Element Methods for Viscous Incompressible Flows, Academic Press, Boston, 1989.
11. M. D. GUNZBURGER, ED., Flow Control, IMA Vol. Math. Appl. 68, Springer-Verlag, New York, 1995.
12. M. D. GUNZBURGER AND S. L. Hou, Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses, SIAM J. Numer. Anal., 29 (1992), pp. 390-424.
13. M. D. GUNZBURGER AND R. A. NICOLAIDES, EDS., Incompressible Computational Fluid Dynamics, Cambridge University Press, Cambridge, UK, 1993.
14. M. HEINKENSCHLOSS AND L. N. VICENTE, Analysis of Inexact Trust-Region SQP Algorithms, Technical report TR99-18, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1999.
15. L. S. Hou, Analysis and Finite Element Approximation of Some Optimal Control Problems Associated with the Navier-Stokes Equations, Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA, 1989.
16. L. S. HOU AND S. S. RAVINDRAN, Numerical approximation of optimal flow control problems by a penalty method: Error estimates and numerical results, SIAM J. Sci. Comput., 20 (1999), pp. 1753-1777.
17. C. T. KELLEY AND E. W. SACHS, Truncated Newton methods for optimization with inaccurate functions and gradients, J. Optim. Theory Appl., 116 (2003), pp. 83-98.
18. C. T. KELLEY AND D. E. KEYES, Convergence analysis of pseudo-transient continuation, SIAM J. Numer. Anal., 35 (1998), pp. 508-523.
19. F. LEIBFRITZ AND E. W. SACHS, Inexact SQP interior point methods and large scale optimal control problems, SIAM J. Control Optim., 38 (1999), pp. 272-293.
20. S. G. NASH AND A. SOFER, Linear and Nonlinear Programming, McGraw-Hill, New York, 1996.
21. J. NOCEDAL AND S. J. WRIGHT, Numerical Optimization, Springer-Verlag, New York, 1999.
22. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.
23. K. SCHITTKOWSKI, The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function, Numer. Math., 38 (1981), pp. 83-114.
24. T. STEIHAUG, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626-637.
25. H. YAMASHITA, A globally convergent constrained quasi-Newton method with an augmented Lagrangian type penalty function, Math. Program., 23 (1982), pp. 75-86.