Software for limited memory restarted $l^p$-$l^q$ minimization methods using generalized Krylov subspaces

Alessandro  Buccini; Lothar  Reichel

doi:doi:10.1553/etna_vol61s66

Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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Software for limited memory restarted $l^p$-$l^q$ minimization methods using generalized Krylov subspaces

Alessandro Buccini,

Lothar Reichel

ETNA - Electronic Transactions on Numerical Analysis, pp. 66-91, 2024/07/03

doi: 10.1553/etna_vol61s66

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doi:10.1553/etna_vol61s66

Abstract

This paper describes software for the solution of finite-dimensional minimization problemswith two terms, a fidelity term and a regularization term. The sum of the $p$-norm of theformer and the $q$-norm of the latter is minimized, where $0 < p,q\leq 2$. We note that the“$p$-norm” is not a norm when $ 0< p < 1$, and similarly for the “$q$-norm”. This kind ofminimization problems arises when solving linear discrete ill-posed problems, such ascertain problems in image restoration. They also find applications in statistics.Recently, limited-memory restarted numerical methods that are well suited for the solutionof large-scale minimization problems of this kind were described by the authors in[Adv. Comput. Math., 49 (2023), Art. 26]. Thesemethods are based on the application of restarted generalized Krylov subspaces. This paperpresents software for these solution methods.

Keywords: $l^p$-$l^q$ minimization, inverse problem, regression, iterative method

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Published Online: 2024/07/03 15:00:46

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Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

Software for limited memory restarted $l^p$-$l^q$ minimization methods using generalized Krylov subspaces

Abstract