  The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one
of the most widely used algorithms in the literature. However, despite its
optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in
practice its performance is not as desired owing to the (local) oscillatory
behaviour. Over the years, various approaches are proposed to overcome this
drawback of FISTA, in this paper, we propose a simple yet effective
modification to the algorithm which has two advantages: 1) it enables us to
prove the convergence of the generated sequence; 2) it shows superior practical
performance compared to the original FISTA. Numerical experiments are presented
to illustrate the superior performance of the proposed algorithm.
