Affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods

SIAM Journal on Control and Optimization

Volumn 41, Issue 3, 2003, Pages 875-899

  Volkwein, S ^a   Weiser, M ^b  

^a UNIVERSITY OF GRAZ   (Austria)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Affine invariant norms; Burgers' equation; Multiplier methods; Nonlinear programming

Indexed keywords

CONSTRAINT THEORY; ERROR ANALYSIS; NONLINEAR PROGRAMMING; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

AFFINE INVARIANT CONVERGENCE ANALYSIS; BURGERS EQUATION; HILBERT SPACES; KUHN-TUCKER EQUATIONS;

LAGRANGE MULTIPLIERS;

EID: 0037860830     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012900383089     Document Type: Article

References (19)

1. R. E. Bank and D. J. Rose, Global approximate newton methods, Numer. Math., 37 (1981), pp. 279-295.
2. D. Braess, P. Deuflhard, and K. Lipnikov, A subspace cascadic multigrid method for mortar elements, Numer. Math., to appear.
3. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5: Evolution Problems I, Springer, Berlin, 1992.
4. R. S. Dembo, S. C. Eisenstat, and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal., 19 (1982), pp. 400-408.
5. P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms, Springer, to appear.
6. P. Deuflhard and G. Heindl, Affine invariant convergence theorems for Newton's method and extensions to related methods, SIAM J. Numer. Anal., 16 (1979), pp. 1-10.
7. P. Deuflhard and M. Weiser, Local inexact Newton multilevel FEM for nonlinear elliptic problems, in Computational Science for the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzigibbon, J.-L. Lions, J. Périaux, and M. Wheeler, eds., Wiley, New York, 1997, pp. 129-138.
8. P. Deuflhard and M. Weiser, Global inexact Newton multilevel FEM for nonlinear elliptic problems, in Multigrid Methods V, Lecture Notes in Comput. Sci. and Engrg. 3, W. Hackbusch and G. Wittum, eds., Springer, Berlin, 1998, pp. 71-89.
9. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer, Berlin, 1980.
10. A. Hohmann, Inexact Gauss Newton Methods for Parameter Dependent Nonlinear Problems, Ph.D. thesis, Dept. Math. and Comput. Sci., Free University of Berlin, Germany, 1994.
11. K. Ito and K. Kunisch, Augmented Lagrangian-SQP-methods in Hilbert spaces and application to control in the coefficients problems, SIAM J. Optim., 6 (1996), pp. 96-125.
12. D. G. Luenberger, Optimization by Vector Space Methods, Wiley, New York, 1969.
13. H. Maurer and J. Zowe, First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math. Programming, 16 (1979), pp. 98-110.
14. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
15. S. Volkwein, Mesh-independence for an augmented Lagrangian-SQP method in Hilbert spaces, SIAM J. Control Optim., 38 (2000), pp. 767-785.
16. S. Volkwein, Optimal and Suboptimal Control of Partial Differential Equations: Augmented Lagrange-SQP Methods and Reduced-Order Modeling with Proper Orthogonal Decomposition, Grazer Math. Ber. 343, Karl-Franzens-Universität Graz, Graz, Austria, 2001.
17. S. Volkwein, Mesh-independence of Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates, Optim. Methods Softw., 17 (2002), pp. 77-111.
18. S. Volkwein, Second-order conditions for boundary control problems of the Burgers equation, Control Cybernet., 30 (2001), pp. 249-278.
19. E. Zeidler, Nonlinear Functional Analysis and Its Applications, Vol. I, Springer, New York, 1986.