On weakly nonlinear inverse problems

SIAM Journal on Applied Mathematics

Volumn 56, Issue 2, 1996, Pages 542-572

  Chavent, G ^a   Kunisch, K ^b  

^a INRIA   (France)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Geometric stability theory; Nonlinear ill posed inverse problems; Semilinear equations; Stability theory for nonlinear least squares problems; Tikhonov regularization

Indexed keywords

ASYMPTOTIC STABILITY; DIFFUSION; GEOMETRY; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

GEOMETRIC STABILITY THEORY; NONLINEAR ILL POSED INVERSE PROBLEMS; SEMILINEAR EQUATIONS; TIKHONOV REGULARIZATION;

INVERSE PROBLEMS;

EID: 0030127690     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994267444     Document Type: Article

References (15)

1. J. BAUMEISTER, Stable Solutions of Inverse Problems, Vieweg, Braunschweig, 1987.
2. A. BJÖRK, Least squares methods, in Handbook of Numerical Analysis, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1990.
3. G. CHAVENT, Quasi-convex sets and size X curvature condition, application to nonlinear inversion, Appl. Math. Optim., 24 (1991), pp. 129-169.
4. _, New size X curvature conditions for strict quasiconvexity of sets, SIAM J. Control Optim., 29 (1991), pp. 1348-1372.
5. _, A geometrical theory for nonlinear least squares problems, in Control Theory of Distributed Parameter Systems and Application, Lecture Notes in Control and Information Sciences 159, X. Lin and J. Yong, eds., Springer-Verlag, New York, 1991, pp. 14-27.
6. _, A new sufficient condition for the wellposedness of nonlinear least-squares problems arising in identification and control, in Analysis and Optimization of Systems, Lecture Notes in Control and Information Sciences 144, A. Bensoussan and J. L. Lions, eds., Springer-Verlag, New York, 1990, pp. 452-463.
7. G. CHAVENT AND K. KUNISCH, Convergence of Tikhonov regularization for constrained illposed inverse problems, Inverse Problems, 10 (1994), pp. 63-76.
8. _, Regularization in state space, RAIRO Journal on Numerical Analysis, 27 (1993), pp. 535-564.
9. H. ENGL, K. KUNISCH, AND A. NEUBAUER, Tikhonov regularization for the solution of nonlinear illposed problems, Inverse Problems, 5 (1989), pp. 523-540.
10. C. W. GROETSCH, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Research Notes in Mathematics 105, Pitman, Boston, 1984.
11. K. ITO AND K. KUNISCH, Augmented Lagrangian-SQP-methods in Hilbert spaces with application to control in the coefficients problems, SIAM J. Optim., to appear.
12. A. K. LOUIS, Inverse und Schlecht Gestellte Probleme, Teubner, Stuttgart, 1989.
13. J. L. LIONS, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéares, Dunod, Paris, 1969.
14. V. A. MOROZOV, Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, 1984.
15. G. M. TROIANELLO, Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987.