Free Access
Issue
ESAIM: M2AN
Volume 27, Number 5, 1993
Page(s) 535 - 564
DOI https://doi.org/10.1051/m2an/1993270505351
Published online 31 January 2017
  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]

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