As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not converge. Motivated by nonlinear inverse problems with nonsmooth regularization, we propose a new Gauss--Newton-type method with inexact relaxed steps. We prove that the method converges to a set of disjoint critical points given that the linearization of the forward operator for the inverse problem is sufficiently precise. We extensively evaluate the performance of the method on electrical impedance tomography (EIT).


  1. Gauss--Newton
  2. nonsmooth
  3. nonconvex
  4. electrical impedance tomography (EIT)

MSC codes

  1. 35R30
  2. 68U10
  3. 49M15
  4. 90C26

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Supplementary Material

Index of Supplementary Materials

Title of paper: Relaxed Gauss–Newton methods with applications to electrical impedance tomography

Authors: J. Jauhiainen, P. Kuusela, A. Seppänen, and T. Valkonen

File: M132171_01.pdf

Type: PDF

Contents: Additional numerical experiments. Additional reconstruction figures. Additional proximal mappings.


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Information & Authors


Published In

cover image SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Pages: 1415 - 1445
ISSN (online): 1936-4954


Submitted: 27 February 2020
Accepted: 21 May 2020
Published online: 27 August 2020


  1. Gauss--Newton
  2. nonsmooth
  3. nonconvex
  4. electrical impedance tomography (EIT)

MSC codes

  1. 35R30
  2. 68U10
  3. 49M15
  4. 90C26



Funding Information

Academy of Finland https://doi.org/10.13039/501100002341 : 303801
Academy of Finland https://doi.org/10.13039/501100002341 : 314701, 320022
Horizon 2020 Framework Programme https://doi.org/10.13039/100010661 : 764810
Escuela Politécnica Nacional https://doi.org/10.13039/501100012511 : PIJ-18-03

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