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Regularization in state space

G. Chavent; K. Kunisch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 5, page 535-564
  • ISSN: 0764-583X

How to cite

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Chavent, G., and Kunisch, K.. "Regularization in state space." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.5 (1993): 535-564. <http://eudml.org/doc/193714>.

@article{Chavent1993,
author = {Chavent, G., Kunisch, K.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {estimation problem; second order sufficient optimality condition; regularization in state space; nonlinear ill-posed inverse problems; optimization; numerical experiments},
language = {eng},
number = {5},
pages = {535-564},
publisher = {Dunod},
title = {Regularization in state space},
url = {http://eudml.org/doc/193714},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Chavent, G.
AU - Kunisch, K.
TI - Regularization in state space
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 5
SP - 535
EP - 564
LA - eng
KW - estimation problem; second order sufficient optimality condition; regularization in state space; nonlinear ill-posed inverse problems; optimization; numerical experiments
UR - http://eudml.org/doc/193714
ER -

References

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  1. [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. Zbl0679.49027MR1050704
  2. [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. Zbl0702.93070MR1070759
  3. [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). Zbl0776.35077
  4. [4] F. COLONIUS and K. KUNISCH, Output least squares stability in elliptic systems, Appl. Math. and Optimization, 19 (1989) pp. 33-63. Zbl0656.93024MR955089
  5. [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. Zbl0736.49017MR1094323
  6. [6] W. EGARTNER, Augmentierte Lagrange-Verfahren und deren Anwendung auf Inverse Probleme mit H1-und L2-Beobachtungsnorm, Austria. 
  7. [7] H. ENGL, K. KUNISCH and A. NEUBAUER, Tikhonov regularization for the solution of nonlinear illposed problems, Inverse Problems, 5 (1989) 523-540. Zbl0695.65037MR1009037
  8. [8] P. GRISWARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985. Zbl0695.35060
  9. [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). Zbl0728.65100MR1102414
  10. [10] K. ITO and K. KUNISCH, The augmented Lagrangian method for parameter estimation in elliptic systems, SIAM J. Control and Optimization. Zbl0709.93021
  11. [11] K. ITO and K. KUNISCH, On the injectivity of the coefficient to solution mapping for elliptic boundary value problems and its linearization, submitted. Zbl0817.35021
  12. [12] C. T. KELLEY and S. J. WRIGHT, Sequential quadratic programming for certain parameter identification problems, Mathematical Programming (to appear). Zbl0743.65070
  13. [13] K. KUNISCH and E. SACHS, Reduced sqp-methods for parameter identification problems, SIAM J. Numerical Analysis (to appear). Zbl0772.65085MR1191146
  14. [14] O. LADYZHENSKAYA and N. URAL'TSEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  15. [15] D. G. LUENBERGER, Optimization by Vector Space Methods, New York, 1969. Zbl0176.12701MR238472
  16. [16] V. A. MOROZOV, Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, 1984. Zbl0549.65031MR766231
  17. [17] A. NEUBAUER, Tikhonov regularization for nonlinear illposed problems : optimal convergence rates and finite-dimensional approximation, Inverse Problems, 5 (1989) pp. 541-558. Zbl0695.65038MR1009038

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