Limited memory restarted ℓp-ℓq minimization methods using generalized Krylov subspaces

Abstract

Regularization of certain linear discrete ill-posed problems, as well as of certain regression problems, can be formulated as large-scale, possibly nonconvex, minimization problems, whose objective function is the sum of the p th power of the ℓp-norm of a fidelity term and the q th power of the ℓq-norm of a regularization term, with 0 < p,q ≤ 2. We describe new restarted iterative solution methods that require less computer storage and execution time than the methods described by Huang et al. (BIT Numer. Math. 57,351–378, 14). The reduction in computer storage and execution time is achieved by periodic restarts of the method. Computed examples illustrate that restarting does not reduce the quality of the computed solutions.