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Semismooth Newton and quasi-Newton methods in weighted ℓ1-regularization
-
Pham Quy Muoi
,
Dinh Nho Hào
Published/Copyright:
July 2, 2013
Abstract.
We investigate semismooth Newton and quasi-Newton methods for minimization problems arising from weighted ℓ1-regularization. We give proofs of the local convergence of these methods and show how their interpretation as active set methods leads to the development of efficient numerical implementations of these algorithms. We also propose and analyze Broyden updates for the semismooth quasi-Newton method. The efficiency of these methods is analyzed and compared with standard implementations. The paper concludes with some numerical examples that include both linear and nonlinear operator equations.
Keywords: Sparsity regularization; nonlinear
inverse problems; semismooth Newton method; semismooth quasi-Newton
method; Newton derivative
Received: 2013-04-30
Published Online: 2013-07-02
Published in Print: 2013-10-01
© 2013 by Walter de Gruyter Berlin Boston
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- Masthead
- Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems
- On a shape design problem for one spectral functional
- An adjoint method for proving identifiability of coefficients in parabolic equations
- Semismooth Newton and quasi-Newton methods in weighted ℓ1-regularization
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Keywords for this article
Sparsity regularization;
nonlinear
inverse problems;
semismooth Newton method;
semismooth quasi-Newton
method;
Newton derivative
Articles in the same Issue
- Masthead
- Conservation laws in differential geometry of plane curves and for eikonal equation and inverse problems
- On a shape design problem for one spectral functional
- An adjoint method for proving identifiability of coefficients in parabolic equations
- Semismooth Newton and quasi-Newton methods in weighted ℓ1-regularization
- On the iterative inversion of generalized attenuated Radon transforms
