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

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 l(p)-norm of a fidelity term and the qth 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.