Software for limited memory restarted lᵖ-lq minimization methods using generalized Krylov subspaces

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≤ 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.