An inexact SQP method for equality constrained optimization

SIAM Journal on Optimization

Volumn 19, Issue 1, 2008, Pages 351-369

  Byrd, Richard H ^a   Curtis, Frank E ^b   Nocedal, Jorge ^b  

^a UCB 450   (United States)

^b Northwestern University   (United States)

Author keywords

Constrained optimization; Inexact linear system solvers; Krylov subspace methods; Large scale optimization; Sequential quadratic programming

Indexed keywords

EQUALITY-CONSTRAINED OPTIMIZATIONS; EXACT PENALTIES; GLOBAL CONVERGENCES; INEXACT LINEAR SYSTEM SOLVERS; ITERATION MATRICES; KRYLOV SUBSPACE METHODS; LARGE-SCALE APPLICATIONS; LARGE-SCALE OPTIMIZATION; LINE SEARCHES; NONLINEAR PROGRAMS; NUMERICAL RESULTS; SEQUENTIAL QUADRATIC PROGRAMMING; SQP METHODS;

ALGEBRA; CONVERGENCE OF NUMERICAL METHODS; LINEAR SYSTEMS; QUADRATIC PROGRAMMING;

CONSTRAINED OPTIMIZATION;

EID: 55849087520     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/060674004     Document Type: Article

References (23)

1. 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.
2. G. BIROS AND O. GHATTAS, 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 J. Sci. Comput., 27 (2005), pp. 714-739.
3. I. BONGARTZ, A. R. CONN, N. I. M. GOULD, AND PH. L. TOINT, CUTE: Constrained and Unconstrained Testing Environment, ACM Trans. Math. Software, 21 (1995), pp. 123-160.
4. R. H. BYRD, J.-CH. GILBERT, AND J. NOCEDAL, A trust region method based on interior point techniques for nonlinear programming, Math. Program., 89 (2000), pp. 149-185.
5. R. H. BYRD, M. E. HRIBAR, AND J. NOCEDAL, An interior point algorithm for large scale nonlinear programming, SIAM J. Optim., 9 (1999), pp. 877-900.
6. R. H. BYRD AND J. NOCEDAL, An analysis of reduced Hessian methods for constrained optimization, Math. Program., 49 (1991), pp. 285-323.
7. F. E. CURTIS AND E. HABER, Numerical experience with an inexact SQP method for PDE-constrained optimization, in preparation.
8. R. S. DEMBO, S. C. EISENSTAT, AND T. STEIHAUG, Inexact-Newton methods, SIAM J. Numer. Anal., 19 (1982), pp. 400-408.
9. E. D. DOLAN, J. J. MORÉ, AND T. S. MUNSON, Benchmarking Optimization Software with COPS 3.0, Tech. report ANL/MCS-TM-273, Argonne National Laboratory, Argonne, IL, 2004.
10. N. I. M. GOULD, D. ORBAN, AND PH. L. TOINT, CUTEr and sifdec: A Constrained and Unconstrained Testing Environment, revisited, ACM Trans. Math. Software, 29 (2003), pp. 373-394.
11. E. HABER AND U. M. ASCHER, Preconditioned all-at-once methods for large, sparse parameter estimation problems, Inverse Prob., 17 (2001), pp. 1847-1864.
12. S. P. HAN, A globally convergent method for nonlinear programming, 3. Optim. Theory Appl., 22 (1977), pp. 297-309.
13. M. HEINKENSCHLOSS AND L. N. VICENTE, Analysis of inexact trust-region SQP algorithms, SIAM J. Optim., 12 (2001), pp. 283-302.
14. H. JÄGER AND E. W. SACHS, Global convergence of inexact reduced SQP methods, Optim. Methods Softw., 7 (1996), pp. 83-110.
15. C. T. KELLEY, Iterative methods for linear and nonlinear equations: MATLAB codes, 1994, http://www4.ncsu.edu/~ctk/matlab-roots.html.
16. M. LALEE, J. NOCEDAL, AND T. D. PLANTENGA, On the implementation of an algorithm for large-scale equality constrained optimization, SIAM J. Optim., 8 (1998), pp. 682-706.
17. 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.
18. J. NOCEDAL AND S. J. WRIGHT, Numerical Optimization, 2nd ed., Springer Ser. Oper. Res., Springer, New York, 2006.
19. M. J. D. POWELL, Variable Metric Methods for Constrained Optimization, in Mathematical Programming: The State of the Art, Bonn 1982, A. Bachem, M. Grötschel, and B. Korte, eds., Springer-Verlag, Berlin, 1983.
20. E. E. PRUDENCIO, R. BYRD, AND X. C. CAI, Parallel full space SQP Lagrange-Newton-Krylov-Schwarz algorithms for PDE-constrained optimization problems, SIAM J. Sci. Comput., 27 (2006), pp. 1305-1328.
21. Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
22. A. WALTHER, A First-Order Convergence Analysis of Trust-Region Methods with Inexact Jacobians, Tech. report MATH-WR-01-2005, Institute of Scientific Computing, Technische Universitat Dresden, Dresden, Germany, 2005.
23. R. A. WALTZ, J. L. MORALES, J. NOCEDAL, AND D. ORBAN, An interior algorithm for nonlinear optimization that combines line search and trust region steps, Math. Program., Ser. A, 107 (2006), pp. 391-408.