A $\sqrt{2}$-accelerated FISTA for composite strongly convex problems

In this paper, we propose a novel accelerated forward-backward splitting algorithm for minimizing composite convex functions expressed as the sum of a smooth function and a possibly nonsmooth function. When the composite objective is strongly convex, the proposed method achieves a linear convergence rate in objective value that improves the leading constant in the exponent by a factor of $\sqrt{2}$ relative to FISTA and also improves upon the best previously known convergence rate for this problem class. Our convergence analysis remains valid even when one of the two component functions is weakly convex, provided that their sum remains convex. The proposed algorithm is derived by discretizing a continuous-time model of the Information-Theoretic Exact Method (ITEM), an optimal first-order method for unconstrained smooth strongly convex minimization.