Regularization in state space
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) no. 5, p. 535-564
@article{M2AN_1993__27_5_535_0,
     author = {Chavent, G. and Kunisch, K.},
     title = {Regularization in state space},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {27},
     number = {5},
     year = {1993},
     pages = {535-564},
     zbl = {0790.65050},
     mrnumber = {1239815},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1993__27_5_535_0}
}
Chavent, G.; Kunisch, K. Regularization in state space. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) no. 5, pp. 535-564. http://www.numdam.org/item/M2AN_1993__27_5_535_0/

[1] W. Alt, Stability of solutions for a class of nonlinear cone constrained optimization problems, part 2 : application to parameter estimation, Numer. Funct. Anal. and Optimization, 10 (1989) 1065-1076. | MR 1050704 | Zbl 0679.49027

[2] G. Chavent, A new sufficient condition for the wellposedness of nonlinear least-squares problems arising in identification and control. In A. Bensoussan and J. L. Lions, editors, in Analysis and Optimization of Systems, Lecture Notes in Control and Information Sciences, Vol. 144 (1990) pp. 452-463, Springer-Verlag, Berlin. | MR 1070759 | Zbl 0702.93070

[3] G. Chavent and K. Kunisch, A geometrical theory for the L2-stability of the inverse problem in a 1-d elliptic equation from an H1-observation, Appl. Math. and Optimization (to appear). | Zbl 0776.35077

[4] F. Colonius and K. Kunisch, Output least squares stability in elliptic systems, Appl. Math. and Optimization, 19 (1989) pp. 33-63. | MR 955089 | Zbl 0656.93024

[5] F. Colonius and K. Kunisch, Stability of perturbed optimization problems with application to parameter estimation, Num. Func. Analysis and Optimization, 11 (1990) pp. 873-915. | MR 1094323 | Zbl 0736.49017

[6] W. Egartner, Augmentierte Lagrange-Verfahren und deren Anwendung auf Inverse Probleme mit H1-und L2-Beobachtungsnorm, Austria.

[7] H. Engl, K. Kunisch and A. Neubauer, Tikhonov regularization for the solution of nonlinear illposed problems, Inverse Problems, 5 (1989) 523-540. | MR 1009037 | Zbl 0695.65037

[8] P. Grisward, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985. | Zbl 0695.35060

[9] K. Ito, M. Kroller and K. Kunisch, A numerical study of the augmented Lagrangian method for the estimation of parameters in elliptic systems, SIAM J. on Sci. and Stat. Computing (to appear). | MR 1102414 | Zbl 0728.65100

[10] K. Ito and K. Kunisch, The augmented Lagrangian method for parameter estimation in elliptic systems, SIAM J. Control and Optimization. | Zbl 0709.93021

[11] K. Ito and K. Kunisch, On the injectivity of the coefficient to solution mapping for elliptic boundary value problems and its linearization, submitted. | Zbl 0817.35021

[12] C. T. Kelley and S. J. Wright, Sequential quadratic programming for certain parameter identification problems, Mathematical Programming (to appear). | Zbl 0743.65070

[13] K. Kunisch and E. Sachs, Reduced sqp-methods for parameter identification problems, SIAM J. Numerical Analysis (to appear). | MR 1191146 | Zbl 0772.65085

[14] O. Ladyzhenskaya and N. Ural'Tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. | MR 244627 | Zbl 0164.13002

[15] D. G. Luenberger, Optimization by Vector Space Methods, New York, 1969. | MR 238472 | Zbl 0176.12701

[16] V. A. Morozov, Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, 1984. | MR 766231 | Zbl 0549.65031

[17] A. Neubauer, Tikhonov regularization for nonlinear illposed problems : optimal convergence rates and finite-dimensional approximation, Inverse Problems, 5 (1989) pp. 541-558. | MR 1009038 | Zbl 0695.65038