  A previous authors' paper introduces an accelerated composite gradient (ACG)
variant, namely AC-ACG, for solving nonconvex smooth composite optimization
(N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local
upper curvature of the N-SCO problem by using the average of the observed
upper-Lipschitz curvatures obtained during the previous iterations, and uses
this estimation and two composite resolvent evaluations to compute the next
iterate. This paper presents an alternative FISTA-type ACG variant, namely
AC-FISTA, which has the following additional features: i) it performs an
average of one composite resolvent evaluation per iteration; and ii) it
estimates the local upper curvature by using the average of the previously
observed upper (instead of upper-Lipschitz) curvatures. These two properties
acting together yield a practical AC-FISTA variant which substantially
outperforms earlier ACG variants, including the AC-ACG variants discussed in
the aforementioned authors' paper.
