Scaled, Inexact, and Adaptive Generalized FISTA for Strongly Convex Optimization

We consider a variable metric and inexact version of the fast iterative soft-thresholding algorithm (FISTA) type considered in [L. Calatroni A. Chambolle, SIAM J. Optim., 29 (2019), pp. 1772--1798; Chambolle T. Pock, Acta Numer., 25 (2016), 161--319] for minimization sum two (possibly strongly) convex functions. The proposed is combined with an adaptive (nonmonotone) backtracking strategy, which allows adjustment algorithmic step-size along iterations order to improve convergence speed. prove linear result function values, depends on both strong convexity moduli functions upper lower bounds spectrum operators. validate algorithm, named Scaled Adaptive GEneralized FISTA (SAGE-FISTA), exemplar image denoising deblurring problems where edge-preserving total variation (TV) regularization Kullback--Leibler-type fidelity terms, as common applications signal-dependent Poisson noise assumed data.