In this paper, we consider an unconstrained composite convex optimisation problem.
We propose an inertial forward–backward algorithm derived from an implicit–
explicit discretisation of a second-order dynamical system with Hessian-driven damping.
For α ≥ 3, we establish an O(1/d^2) convergence rate for the objective value
gap. Furthermore, when α > 3, we prove that the iterative sequence generated by
the proposed method converges to a minimiser, and that the objective residual admits
an improved rate of o(1/d^2). Numerical experiments are provided to illustrate the
effectiveness of the proposed approach.