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

• Published in: Advances in computational mathematics Vol. 49; no. 2
• Main Authors: Buccini, Alessandro, Reichel, Lothar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2023; Springer Nature B.V
• Subjects: Computation; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Ill posed problems; Iterative methods; Iterative solution; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Optimization; Regularization; Restarting; Subspaces; Visualization; 65R32; 65F10; minimization; Regression; Iterative method; 90C26; -; Inverse problem
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-023-10020-8

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 q th power of the ℓ q -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.