  We address composite optimization problems, which consist in minimizing the
sum of a smooth and a merely lower semicontinuous function, without any
convexity assumptions. Numerical solutions of these problems can be obtained by
proximal gradient methods, which often rely on a line search procedure as
globalization mechanism. We consider an adaptive nonmonotone proximal gradient
scheme based on an averaged merit function and establish asymptotic convergence
guarantees under weak assumptions, delivering results on par with the monotone
strategy. Global worst-case rates for the iterates and a stationarity measure
are also derived. Finally, a numerical example indicates the potential of
nonmonotonicity and spectral approximations.
