Explore a 23-minute conference talk from the "One World Optimization Seminar in Vienna" workshop held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the convergence analysis of a nonmonotone forward-backward splitting method for tackling nonsmooth composite problems in Hilbert spaces. Examine the objective function, which combines a Fréchet differentiable function and a lower semicontinuous convex function, commonly found in optimization problems involving nonlinear partial differential equations with sparsity-promoting cost functionals. Learn about the algorithm's convergence and complexity, including linear convergence under quadratic growth-type conditions. Gain insights from numerical experiments that validate the theoretical findings presented in this advanced mathematical optimization talk.