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Zbl 0790.65050
Chavent, G.; Kunisch, K.
Regularization in state space. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 27, No.5, 535-564 (1993). ISSN 0764-583X

The objective of this article is the introduction and analysis of regularization in state space for nonlinear ill-posed inverse problems. Many results in the abstract as well as in the numerical treatment of optimization problems rely on the ``second order sufficient optimality condition'' which, roughly speaking, is the positivity of the Hessian of the cost functional at the minimizer. The last section of the paper contains several numerical experiments demonstrating that regularization in state space can be an effective tool for solving nonlinear ill-posed inverse problems.
[G.Dimitriu (Iaşi)]

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
65K05 Mathematical programming (numerical methods)
90C30 Nonlinear programming
47J25 Methods for solving nonlinear operator equations (general)

Keywords: estimation problem; second order sufficient optimality condition; regularization in state space; nonlinear ill-posed inverse problems; optimization; numerical experiments

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