  In this paper we propose two proximal gradient algorithms for fractional
programming problems in real Hilbert spaces, where the numerator is a proper,
convex and lower semicontinuous function and the denominator is a smooth
function, either concave or convex. In the iterative schemes, we perform a
proximal step with respect to the nonsmooth numerator and a gradient step with
respect to the smooth denominator. The algorithm in case of a concave
denominator has the particularity that it generates sequences which approach
both the (global) optimal solutions set and the optimal objective value of the
underlying fractional programming problem. In case of a convex denominator the
numerical scheme approaches the set of critical points of the objective
function, provided the latter satisfies the Kurdyka-\L{}ojasiewicz property.
