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

This paper describes software for the solution of finite-dimensional minimization problems with two terms, a fidelity term and a regularization term. The sum of the p-norm of the former 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 of minimization problems arises when solving linear discrete ill-posed problems, such as certain problems in image restoration. They also find applications in statistics. Recently, limited-memory restarted numerical methods that are well suited for the solution of large-scale minimization problems of this kind were described by the authors in [Adv. Comput. Math., 49 (2023), Art. 26]. These methods are based on the application of restarted generalized Krylov subspaces. This paper presents software for these solution methods.