Efficiency of line search strategies in interior point methods for linearly constrained signal restoration

Abstract

We discuss in this paper the influence of line search on the performances of interior point algorithms applied for constrained signal restoration. Interior point algorithms ensure the fulfillment of the constraints through the minimization of a criterion augmented with a barrier function. However, the presence of the barrier function can slow down the convergence of iterative descent algorithms when general-purpose line search procedures are employed. We recently proposed a line search algorithm, based on a majorization-minimization approach, which allows to handle the singularity introduced by the barrier function. We present here a comparative study of various line search strategies for the resolution of a sparse signal restoration problem with both primal and primal-dual interior point algorithms.