An inexact quasi-Newton algorithm for large-scale l1 optimization with box constraints

In this paper, we develop an inexact quasi-Newton algorithm for l(1)-regularization optimization problems subject to box constraints. The algorithm uses the identification technique of the proximal gradient algorithm to estimate the active set and free variables. To accelerate the convergence, we utilize the inexact quasi-Newton algorithm to update free variables. Under certain conditions, we show that the sequence generated by the algorithm converges R-linearly to a first-order optimality point of the problem. Moreover, the corresponding sequence of objective function values is also linearly convergent. Experiment results demonstrate the competitiveness of the proposed algorithm. (C) 2023 IMACS. Published by Elsevier B.V. All rights reserved.